Is all 6061-T6 equal?

On the longevity question, failure isn't just about complete failure. Lugged steel frame bikes used to eventually go 'soft' over time, and be far less fit for use than when they were new. In the case of a lightweight frame this could be after just a couple of seasons of racing. I owned one of the first 6061 frames, a Cannondale 2.0. I rode and raced (and occasionally crashed) that for 20 years and it was as solid as the day it was built when I finally retired it which only happened when a crash tore off the rear derailleur. The frame was one of the original versions and had solid aluminium drop outs so was irreparable. 

Large tube welded alloy frames are very durable. Modern ones (like a Cannondale Synapse) also offer really good levels of comfort, a feature which my dinosaur notably lacked Trek and Giant also make excellent versions that I would have no qualms about buying second hand even if 10 yrs old.

No, all frames are definitely not equal, irrespective of the material used.

A builder/designer can choose based on various qualities like wall thickness and butting (compare a seat stay with the downtube, for instance), and that's before you consider the differences in stiffness/compliance and the ride feel by altering the geometry.

The difference will depend on the design/quality of your existing frame and what you're comparing it with.

Your decision may also depend on how keen you are to replace it. Perhaps you really like it, in which case you may want to continue riding on it. If that's the case then I'd weigh up the cost of upgrading components against the cost of a new bike with a similar specification.

Unlike steel and titanium, fatigue builds up in aluminium much more than it does in other metals. Unless you subject it to a fatal blow, steel ill not suddenly fail. Aluminium in effect stores up all it's sub-fatal impacts and when they build up to the fatal level it may well break. Modern alloying technology has mitigated this somewhat but I've personally never felt particularly comfortable with aluminium as a frame material.

Realistically, if I bought an aluminium framed bike would it ever break? Probably not but I prefer to stick to steel, titanium or carbon.

Yes, all aluminium alloy frames will fatigue and eventually fail  (google "fatigue limit"). How far into the future that happens depends on a number of variables - e.g. tube wall thickness, weight of rider, road surface etc.

I think you are overthinking it a bit. 6061 is an excellent material to make bike frames out of as it is relatively light and strong. Whihc is why a huge number of bikes are made from this material worldwide. More modern construction methods such as hydroforming and the like are often used to make the frame lighter and potentially give a better ride quality. I don't know if they last any longer.

You can use the same material to make a cheap frame or an expensive one. A cheap frame might not be very well aligned, for example.  6000 series alumium alloys require heat treatment after welding, but the fact that you are talking about T6 frames will mean that they will have had a post weld temper, and so the material properties of all 6061-T6 frames will be the same.

6061 T6 is the grade of aluminium used in the tubes and is (to all intents and purposes) exactly the same from bike to bike. What tubes and how they were made / drawn and how they were then created into a bike are the important factors. So, the short answer to your question "are all 6061 frames created equal?" No. They're not. The material is equal, but that is it. As others have suggested, getting reputable brands from known frame makers is going to have a big impact on the performance and reliabiity of the frame. 

A more expensive 6061 frame might be lighter due to butting, but in my opinion two 6061 frames of similar weight and geometry are going to be the same. It's the brand name painted on the side that most people have an issue with.

The link below explains why 6061 is used for bike frames. T6 grade is used due to its light weight, ease of building (welding) and resistance to corrosion (spoke and stem holes). Cheap would fall into the price category not material properties (the latter further explained below)

http://bike-advisor.com/bicycle-guides/aluminum-frames-6061-vs-7005-whic...

"Are all 6061-T6 frames not equal? I just want to know how to grade a 6061-T6 frame if they vary so much."

Who and how its built should be considered. Surely an inexpensive cheap Chinese frame vs one from a reputable builder comes into play. When and if problems occur who stands behind their warranty? Who eats the transportion/shipping fees? Who guarantees what you're buying is an 6061-T6 frame not some other alloy? 

"I don't need to know why 6061-T6 is not as good as Steel/Carbon/Ti"

Frame stiffness, weight and compliance are your factors. Steel is the heaviest yet stiff and very compliant. Also steel can handle massive amounts of abuse. Ti is lighter than steel and compliant but has a tendency to flex. Alloy is lighter than Ti but has less compliance, the ride is harsher. Carbon gives you light weight, stiffnes, and compliance but cannot handle abuse. Also keep in mind cheap carbon lacks compliance.

Inspect the frame first hand. If buying from an LBS ask the mechs their opinions. Do research on the builder/mfg - reviews, etc.

Hope this answers some of your questions.