OK, but tell me this. Saying stuff like that is all good, but is it one of those things where "on paper" it is better but not so much in reality?
I'm trying to figure out if it really is a case that, yes, you should absolutely try to go the 5D route for video because it is worth it in terms of the image you get.
Yes, I used to have a T2i and have had a 5DII for over a year and I shoot video 90% of the time. There is a significant difference in low-light capability between the two, generally the larger the sensor, the better it does in low light.
For instance, with the T2i, ISO800 is pretty much the limit for shooting acceptable video, and even at 800 there is a fair mount of noise. But with the 5D you can get away with ISO 1600 all day, and will look less noisy than a T2i at ISO 800, so there is a pretty big difference. But with the 5D you'll also get more shallow depth of field, and your lenses will look less "zoomed" than they do on your 60D. Your wide angle lenses will actually look wide instead of medium telephoto-ish. Also the 5DII handles rolling shutter much better than the 60D.
As for whether it's worth it or not to buy a 5DIII, I'd honestly say no. If you aren't even sure of the differences between an FF and APS-C sensor I would guess that you aren't doing work at the level that would necessitate purchasing a brand new $3500 camera. You would be better off buying new glass and upgrading bodies once the price of the 5DIII drops, or you could get a 5DII and it would still be a big improvement over the 60D.