OP, before you shell out the cash for a new DSLR, I want to make sure you took in Photo Chick's point about images being 90% photographer and 10% camera. I'd hate for you to spend that amount of money, and then be disappointed by the results.
Let me pause to say that I honestly don't mean this reply to sound preachy. I'm actually adding this paragraph after the fact, because I just read what I wrote, and I'm afraid it does come off that way. A $650 camera is a pretty significant investment, though, and I just want to make sure you realize it won't magically transform the photos you take.
A camera is a tool, and a tool is only as good as the person using it. I'll try to explain my point by likening it to another tool; a saw, for example.
If you go to Home Depot and look at table saws, you might find a basic, portable unit for about $150. Sitting next to it may be one that costs $2,500 that includes a combination of table saw, lathe, sanding belt, jigsaw, and drill press.
A skilled carpenter who's been practicing woodworking for years could probably take that cheap $150 table saw and build a really nice table. It wouldn't be fancy, but it would be nicely made and beautiful. The same skilled carpenter could use the more expensive tool to make a truly amazing table. He'd know how to use all the different bells and whistles on the more expensive tool to their best advantage, and the result would be a fine crafted work of art. People would love either table, and would probably pay to have them in their houses.
A weekend do-it-yourselfer like myself would take the $150 table saw and I'd probably be able to make a table (of sorts). It likely wouldn't be that pretty, wouldn't be too stable, and would certainly not be something I'd want to display in my living room. But it would be a table; something good enough that I could use in the garage or in a garden shed, perhaps. If I got the fancy tool, I could do a better job of building a table. It would look better than my attempt with the cheaper tool, but still wouldn't be up to the standard of either of the skilled woodworker's tables. If I wanted to match his product, I'd need to put in the work of reading about woodworking, possibly taking some classes, and getting lots of hands-on experience.
If you want to take a DSLR out of the box, leave it in full automatic mode, and use it the same way you've used your point-and-shoot camera, you will see some improvements. The optics and sensors in the camera will indeed give you better pictures than you got with your Fuji. It's an expensive way to achieve the amount of improvement you'll see, though. There are lots of people who use DSLRs in this fashion who are very happy with them. If this is you, the question between the T3 and the T4i (or even the Nikon you mention) might be good reasoning to lean you toward the cheaper DSLR options. All of the camera's you mention are probably pretty much equal at this level. They'll all create wonderful snapshots for you.
If you think you might be on the cusp of wanting to pursue a higher level of photo taking and become a photography hobbyist, the T4i is absolutely a wonderful starter DSLR. It has lots of those bells and whistles I was talking about. You'll also want to look at some software to use to "develop" or "tweak" you photographs after you get them into your computer. Dedicate some time to read a few books, watch some online training videos, and spend lots of time practicing with your camera, and you'll be amazed at how quickly you can move from snapshots that are passable for a vacation album to shots you want to frame and hang in your house as artwork. I took this step of wanting to learn how to use all the buttons on my DSLR (a Canon Rebel XT) about two years ago, and have had an absolutely wonderful time learning since. It's become a hobby that I love, and I've since moved to a Canon 60D.
The folks on this board a very helpful in recommending books and web sites and other learning opportunities, should you choose to go in that direction.
In any case, have a great time at the Contemporary. Be sure to come back and show us some photos!