The T2i is smaller and a lot lighter than the 6D. It has a pop-up flash; the 6D does not. But the 6D has Wi-Fi to an iPhone which allows me to shoot at weird angles, and GPS for geo-tagging. The 6D cannot take EF-S lens.
It's felt to me as a natural progression. The one area that blind-sided me just a little is with the accessories. As the 6D is bigger and much heavier, I didn't want to risk using my cheaper tripod that I had purchased for my T2i with the 6D. My camera backpack that I used for my T2i isn't so perfect with the larger camera body and now larger lenses. etc etc etc. What I ended up doing was keeping all the accessories that I had purchased for the T2i stays with my T2i. Had to buy net new for the 6D. And you'll find that the accessories that you buy for the 6D will cost you more than what you would have spent for the T2i. From a technical perspective, if you have figured out how to use the T2i, you won't have problems with the 6D. Everything is basically the same, the 6D just does everything a bit better, faster and quieter. You will gain some functionality while not losing any. It's a serious upgrade but not an intimidating one. In my experience, my T2i prepared me for this excellent camera!
The major change is the useable iso of the 6D. The 6D is useable up to 6000 iso and I'm not exaggerating. I came from a T2i, which is an incredible camera but the shots with the 6D have notably more color, contrast and detail.
User interface is about the same. The outcome is a world apart.
In one word, the change you will see/feel is "Quality" - period. If you are satisfied with the quality of images you get from your T2i, you might as well stick with it and perhaps spend your money on better quality lenses or a Speedlite. With a full-frame camera, everything is going to be that much more expensive just as the 6D body is more expensive than the T2i body. You will need newer, more expensive full-frame lenses. Also you will most likely want to move toward shooting RAW and establish a RAW files processing workflow which may require upgraded computer/software. There were many "hidden" costs to owning a full-frame camera than just the initial purchase price of the body itself.
Two big changes: 1, the effect range of the lenses increases which can be useful for things at the telephoto end (200mm -> 300mm effective) where as the reverse is true for wide angle lenses. 2. Depth of field increases so with a FF camera it's easier to isolate subjects with focus. Generally biggest diff though is low light performance. With the 6D you can shoot w/out flash in really dim light w/out much noise.