In "film" parlance, the 5d3 will give you a finer, better quality "grain" as if from a top-quality negative film versus a cheap off-brand. It will hold up better in more challenging circumstances too. Less noise, more light collected. You are correct in that at 8x10 type print size, there won't be much difference in a well-exposed shot.
I have a 16x10 print from my old 30d that looks great, with less than half the resolution of a 650d.
However, take that shot wrong (over/underexposed in particular) and it'll be harder to fix. Crop into it and print or view that portion, and you'll start to see the difference. In theory at least, the FF sensor collects a stop and a half more light, so it's like using film at twice the ISO rating for the same 'grain' -- or that you can get away with half the light at the same ISO.
The quality of the lens in front of the camera is at least as important as the sensor behind that lens. It also matters whether you have the right lens(es) for the subject matter you are shooting. You may or may not have EF mount lenses (or L series within that) for your film bodies - but it sounds like you may get more 'mileage' from spending your money on suitable glass for the trip.
There is nothing wrong with a 650D as a travel camera. I'd rather have one of those and the 'right' lenses than a more expensive body and only one lens of the 'wrong' focal length or a cheap zoom because that's all I could afford.
You are probably aware that the 650D has a different FoV due to the crop sensor, which changes the 'apparent' focal length.
If you can afford the 5D and have the glass already, go for it. When you sit down to post-process the images afterwards, you won't be sorry. I just bought a 5d Mark III myself, with a small collection of L lenses which are *specifically* what I need for my subject matter (24-105, 70-300L, 100L). They are a compromise, but cover my needs for much less than I would have paid (24-70 II, 70-200 II, 1.4x, 2.0x, 100L.)
For me, it was Hobson's Choice: I wanted a FF camera, didn't like the Nikons, and couldn't afford the 1DX by a long stretch. As soon as the 6D turned out to have an AF system that is useless for my needs, I jumped on the first decent offer for a 5d Mark III, and I'm delighted with the results.
Both cameras will provide "OK" results from basic EF lenses, and better results from better EF lenses. A dodgy lens will produce images that look blurry and smeared on both cameras when you zoom in to 1:1. I can even see that on the 8.5MP 30d. To really see the difference, try shooting in challenging light or with a really good quality lens. At least you don't have to deal with EF-S lenses coming from film! Your 70-200 f4 IS is a pretty good start.
Good luck and happy shooting. I dare say the 6d with 24-105L was MADE for you.