Gravel vs road gearing... less force to pedal?

An advantage of a tall geared road bike vs a tall geared trail bike is topography. On the road during a descent there isn't that need to have an accelerating gear ratio because roads aren't weaving trees and bumps and such similar loves.
Hence if you have a capable ratio selection to climb and motor along flats with; I ;not being a racer, you might be lazy like many of us and after a peak, hit top cog and regard less concerning acceleration because you're underway and may input light or heavy stance on your crank and enjoy the distance. Ohh look a tree whoo it's the other side of the gutter.
50/11 is pretty tall man. 53/13 similar. Both plenty enough to push wind coming down or slow crank and recover

Advantage of a double over a single up front is the smaller jumps in the cassette for the same coverage of ratios, which can help maintain cadence.  For the road that's more important however not everyone is sensitive to it.  If you frequently find yourself running out of top end gears then go 52-36.  If not, compact or below will likely suit you better and give lower drive train losses as others have said.  Drive train losses are not insignificant but if you're using knobblies then road tyres will give you the biggest benefit.

Everyone has their preferred cadence and finding the gears that work for you and your type of riding is going to help you.  If it's flat, you're bigger and you like to pedal at 80rpm then larger chain rings, if it's proper hilly, you're Quintana-esque and you like to spin then smaller.  There is no right answer.

For the same ratio, ignoring utterly miniscule drivetrain efficiency differences, the pedalling effort is the same at the same speed. Overall your 42 chain ring set up is about 1-2 gears lower than your 52:36 would end up, so easier overall, but at any given cadence for the same speed, it is just as easy / hard to pedal on either combo

I am not quite sure what you are getting at but just bear in mind that it takes a very very fit rider to sustain power through either a 50-11 or 52-11 combo for long periods. If you look at the wear on the average riders cassette, its all in the middle. You maybe spend 3% of your ride in that absolute top gear (50-11 with a compact, for example). So its barely worth having. More usable gearing in terms of front chainrings is 46/32, as you can easily envisage spending a good amount of time turning the 46-11 combo on a nice A road run, and the smaller ring means you can run a tighter block at back (11-28 maybe) which eliminates some of the indelicate shift action getting up to/coming off of a 32 tooth sprocket.

Can you get some test rides on road bikes so your thinking isn't all theoretical? You might just love the road bike experience. 

Mechanical advantage isn't always an advantage.
Take a car. Like a human the car has a torque band. At a climb, we the pilot has choice. Drop it back or hold top cog . If we hold top cog we slow and then stall yet if we had dropped it back we could have easily climbed the hill. Hence the mechanical advantage became an impossible task.
We all get head winds, tail winds, gradients. The flatter your routes the tighter your groups or your prepared to walk up a swift descent.
The cogs on that will get you up and down, reads really sweet broad range but unless you're an Olympian peddling 150km pre work daily or similar, I guess 52-11 would be used as rather swift descents.

Don't worry about gearing efficiency, drivetrain losses are not significant with derailleur gears assuming they're not faulty or gunged up. Stop thinking about direct, indirect, whatever.

What does count is having the range of gears you need.  Your proposed 52/36 11/30 setup would work fine although 52-11 is a very tall gear more suited to racing than normal riding around. I'd prefer a 50-34 up front but it's not a big deal.

Di2, or EPS as I prefer to call it, might be a luxury but you'll absolutely love it.

I am going to assume you've ridden your gravel on the road with gravel tires. With this in mind and knowing good road tires would improve rolling resistance how much gear changes are you looking for, and how often do you spin on the smallest cog?

For example on gear rations:

1. Running 52/12 is 8.7%. Running 42/10 is 8.5% - .2% difference

                       52/11 is 9.5% - 1% difference

2. Running 50/11 is 9.2%. Running 42/10 is 8.5% - .7% difference

The least expensive option to try is getting good road tires. eg; Conti 4000s II in 25/28mm. Mount them an go ride (if your current rims can take smaller tires). You'll know then if a bigger chain ring is what you want, or not. You'll also know that you can mount the Conti's on your new ride.

It may be a 'completely unscientific question', but it's certainly an interesting one.
Enjoying the responses.

My road bike has 52/36 and 11-32, I use all the gears.  If I lived in the Alps I would be tempted to go proper compact at the front but other wise I think you want a big chainset.

I am old school though, until 3 years ago I rode a 53/39 with 12-28.  I could get up the Sussex hills with that, but I would be painfully slow and out of the saddle to do it.  My friends on compacts would sit and spin and ease away from me.

Short answer, bigger gear up front and smaller gear out back is more mathematically efficient.

Drivetrain efficiency improves as mechanical advantage increases. When you are using the 42 front ring with the 42 cassette, you have no mechanical advantage, therefore, the drivetrain loses are significant.

If you could have a gearing with infinite mechanical advantage (i.e. infinitely large front gear) it will be 100% efficient.

Obviously, you can't have an infinitely large gear ratio.

Chain line is important too, the straighter the chain line, the lower the drivetrain losses. With a 42 tooth, you'll spend more time using the small cogs on the cassette, so the chain line will be better.

By far the most important thing is if the range of gears is suited to your type of riding. You could have the most efficient drivetrain, but if the gear range is wrong, you won't be able to use the gears efficiently.

Your gear choice should be influenced by the speeds you ride at, hence why the gravel bike has lower gearing. My road bike, Canyon Ultimate, has 52/36 with 11-28 - absolutely great for fast road riding, as I use the whole spread of gears over a ride. My commute/winter road bike has 50/34 with 11-32, I don't need such top-end gears as I don't hit really high speeds on commutes and I need to lower gears when I taking it easy up hills (with a full rucksack).

I did the Di2 thing - great for commuting as it guarantees reliable shifting in all weathers, although the buttons are harder to use in winter gloves than mechanical.

I think if you can find a used 6870 Ultegra Di2 group then that's the best option, at worst you'll need to replace the battery.

I've now gone back to a mix of Tiagra and 105 (chainset & front mech) on both my bikes as that's definitely the sweet spot in terms of performance/weight/functionality/price. Unless you're racing you really don't need 11-speed, a 10-speed Tiagra wide-range cassette will do the job.  You do need to know how to set up and service your drivetrain, or be willing to pay your LBS to do it for you (that soon gets old, and drivetrain tuning is pretty easy once you've done it a few times - certainly easier than wheel building, or diagnosing Di2 issuess).

To get back to your question, it doesn't matter what size the rings are, if the development is the same then the same amount of effort will be required. Crank arm length can make a difference to efficiency but that's one for an advanced bike fit to determine.

I don't think the gearing will make as much difference as the difference in tyres and aerodynamics on a road bike vs a gravel bike. In general, drivetrain losses/inefficiencies are tiny, so recreational riders are unlikely to notice any real difference beyond which gear ratio you are using.

Di2 is lovely to use, but in my mind is more of a luxury thing. If you've got the money, then go for it but if you have to dress your children in sackcloth in order to afford it, then maybe a mechanical 105 groupset would be a better spend.

Since upgrading to a Di2 road bike, the biggest difference that I found was hydraulic disc brakes vs calipers. I'd assume that your 4k road bike would be equipped with hydraulics.

I use my gravel bike for all sorts, flirted with 1x but not that into it. I use a 46/34 double for everything now, it's plenty of top end for non racers who aren't putting down a load of watts.

It was also good enough for the guy who won the TCR last year.

Mathematics of powering a bike is fairly simple.
If your mate peddling along with you at the same pedalling rpm. If you were to double the force on your pedals you would double your power output.
Likewise if you were to remain with consistent force on the pedals, by doubling your rpm you would double your power output.

We are mere mortals. We have a limit of force we can comfortably apply to the pedals. Pros know this better than I hence to improve horse power they lower their ratio and increase their rpm at the crank.
Just common cyclists like me don't bother exerting large efforts knowing knees/cranks/peddles will wear faster and increasing rpm at crank is slower at first yet brings thirst to eat properly and use slightly different muscle group coordination.
Per example. If you're riding into the wind and peddling gets harder. A drop of a couple of cogs might result in slightly less effort (about the same) yet twice as fast rpm at peddles. Hence twice horse power.
Therefore, a speed that is about 30% faster!!!!

Big ratios might tend towards downhill sprinting with us non pros.
50/34-11/36 covers a lot of ratios. Already set up hence no need to configure chain length.
Reads awesome bro. (Better than walking up the steep hills. Lol)

I ain't a strong rider. Tall leverage is on the bike primarily to bolt downhill and downwind. 52-10 is heaps tall.
Here I'm waiting on a chain breaker to finish my bike. Tall is 53-13 which I'm guessing will be rarely used. Usage intended is coming down 5-7% grades and long flats with 20+ knots on the back.
But aye, if you can get good pedal rpm on tall cogs,, let me admire your tree stumps. Been commuting solid 2 months, getting more speed with pedal rpm rather than heat on knees.
On an aero 8kg fixed drive 50-16 I find sprints of 40kmph, cruising of less than an hour at 30kmph and all day at 20kmph.
With my tall ratio bike I built that above my strength because our local conditions are a continual downhill road of 25 km and dominant winds that blow me home and blow me along flats and downhill of distances about 30-40km.
With only 10 teeth on rear, a compact 50-34 would be heaps tall!