Why is my hybrid faster than my road bike?

I think we need pics of your positions on both bikes. Maybe you've a good one on the hybrid and a not so good on the road bike ? 

You should be a bit more aero on the road bike - that may not be important going uphill - but on the descents and the flat it will work for you. 

What tyres do you have on each bike? I imagine those on the Hoy are what it came with - Mavic WTS I think. If you have a fast tyre on the hybrid, maybe a Conti GP4000 or the like, they will make a fair difference, as the Mavic tyres seem pretty draggy to me. Try swapping tyres across bikes and try your sample route again.

"And yes, my hybrid is red!!!!"

Well there you go then!!

The point people have been making about the ascents on your hybrid are likely to be less about breathing and cadence, and more about leg angles. The more open your hip angle is the greater power available (a factor of leverage). I haven't read through all the comments, but if your average speed is around 12 mph / 20 kph then your aerodynamic efficiency is likely to be outweighed by comfort / muscular efficiency. This isn't to say that your road bike won't be faster, but if you've ridden your hybrid for a long time, and only just started riding a road bike there iwll be quite a period (months) of your muscles adapting to the new position and improving their efficiency. 

As you say, If you enjoy it, that's the main thing. As for being in a classic racing bike fit position, if your abdomen is gettingin the way of your legs, or your breathing is being constricted, then yes, you will be generally slower. I've helped a lot of generously proportioned middle age ladies to complete a century ride (Taupo Challenge) here in NZ. I do a bike fit for them at the start of the 26 weeks, and then again with about 8 weeks to go. Initially it's for comfort, and we slowly introduce what aero gains we can. They inevitably end up faster over that time, but always it's about comfort rather than speed, as typically these ladies take 7-8 hours to do the century. 

So, if you want to be faster, set your road bike up to largely mimic the set up on your hybrid, and then gradually move that toward a more aero position. 

Good luck

Also, if you enjoy riding the newer bike, then you haven't wasted your money at all.

Think how much faster you will be on a wide bar fat bike!

My money is on it being your position on the bikes. Get a tape measure and take some basic bike fit measurements (e.g. saddle height and reach) and compare the two. Maybe then try tweaking what you can on the road bike to see if you can get it closer to your position on the hybrid and see if that improves your speed?

Alternately, your tyres can make a big difference, especially with different pressures. Too much tyre pressure can slow you down, although I'd be surprised if it makes that much difference going uphill.

Speed (engine aside) is determined by tyre setup, rider's position and up to certain extent weight,  not by what the bike is called.

Following in the same vein as previous commenters, on the steeper hills I'm faster on my XC bike than my road bike because of the gearing. Even 34-32 isn't enough to "comfortably" lug my 220lb frame up a 15% grade. On anything between 5-15% it's mostly weight (unless you can truly acquit yourself uphill) that does the trick. Road bike vs hybrid will be mostly down to the scales. So I wouldn't be surprised on similar times on a fairly hilly course, or even faster times on a particularly punchy affair.

Outside of that, I also agree that repeatably faster is a bit weird. And on the flat the road bike should be noticeably faster than the more upright commuter, unless you're commuting into Roubaix. Comfort, crank length, tyres are all worth looking at, but that should really all be marginal. Anything bad enough on bike fit and position to have that kind of an impact should really be felt or, especially, seen by a bike fitter.

So I'd guess a combination of fitness and mechanical issues. Maybe you've gotten fitter and the mechanical issues on your bike have masked it. I did a couple of shockingly slow times up a climb early in the year, some of which was lack of fitness, but most of which was tyre rub due to a faulty skewer.

"All the way through the ride, but especially on ascents, I am significantly faster!!"

Do you have cadence sensors on both? What chainrings and sprockets do you have on both bikes? How many miles have you done on the Hoy in 18 months?

I'd echo much of what has already been said, but because you're particularly quicker on ascents on your hybrid, I'm wondering whether you're a spinner (more comfortable spinning a faster cadence/smaller gear) and your hybrid lets you do that more easily 1) because of its gearing and 2) because of your position on it.

In other words, as mungecrundle: its range of gears allows you to spin at your favoured cadence in a position that's more naturally suited to you. Also as dottigirl: not everyone is designed to be tipped forward into a 'roadie' tuck. Alternatively, you just might need a bit more 'training' to develop muscles further on the roadie, if you haven't done much mileage on it.

(It could be a bit from column a and a bit from column b (and columns c, d, e...) so good luck with the search)

At any rate, there's more info needed in order to attempt to diagnose over the Web.

Riding on the hoods or top bar should be like riding your hybrid. If it's not then geometry is way off. Only other thing is tyres, and surface sometimes a bigger tyre will roll better over a poor surface.

There was a trend a few years ago for TT riders to ride the most aero shape possible, despite discomfort. And there was confusion when the numbers didn't improve.

That is, even if you're not in pain, if you're stressing your muscles, your performance will suffer. Therefore, I'd look at your position on a bike: are you really comfortable? Do you have pain anywhere after a longer (over 40-60 miles) ride? That's when the weaknesses in a bike fit usually tend to start showing. 

Secondly, do you really feel you're able to put the power in? If you stand, pedal a bit and sit, does your rear land where it should on the saddle? Do you feel you're recruiting your largest muscles?

Are you as upright on your road bike as on your hybrid? Some hybrids do have quite aggressive positions, so transferring to a road bike may not show the normal benefits of of being bent lower.

I'd look at your setup too. Tyre width, pressure, etc. If you're riding too hard a tyre on the road bike, you could feel you're going faster than you are. For ascents, those with a bigger sprocket often spin away from the churners, so if your hybrid has a wider range, that would make sense.

Having said that, some hybrids are a lot faster than you realise. 

Maybe your position is better for your breathing on the hybrid. Try sitting more upright on the climbs on the road bike. You often see people fold themselves up over the bars when battering uphill, crushing their torsos unable to breathe properly. Maybe your hybrid is stopping you from doing that.

I think you need to repeat the experiment over a number of rides and get a rough average. If still a discrepancy then maybe the old bike is simply better set up for you, more comfort often = better efficiency, maybe the gearing is more suited to maintain an efficient cadence?

Faling that:

Is your old bike red? Red bikes are always fatser.

Are you comparing one ride on the Trek with loads of others on the Hoy?  Did you have a tail wind when on the Trek?  How long is the ride?  Is the gearing on the Trek more suited to ascending?  Have you added weighty stuff to the Hoy?

So many factors influence a ride, it's hard to say from what you have said.