Congrats on the jump from the S3 to the T2i. I actually mad the jump from the S3 to the T1i, myself.
One thing I've realized about shooting in RAW, is that you can really bring out some "hidden" colors.
Here's one example. I shot this in RAW, and here is the before and after:
A better look at what the RAW version produced:
But for the sake of argument; I converted the "straight out of the camera" RAW pic directly to JPEG before touching it at all, THEN made adjustments to that first JPEG version:
I tried to get both versions to look very much alike. But one difference you can definitely see, is the orange from the sky. There isn't any orange to be seen in the original RAW, but it was nicely brought during PP.
For "the argument", the orange was a struggle to even just bring out a little. And it still doesn't look nearly as good. This is just a small example, but I hope it helps.
But one reason I really like to shoot in RAW, is for peace of mind. I know I don't have to get exposure or white balance perfect; and I can pretty much just shoot away. In fact, my turning point from shooting just JPEG to shooting in RAW, is when I accidentally left the white balance set to Tungsten for outdoor pics. It was not fun to have to deal with blue tinted pictures.
As far as software, I'm a fan of Lightroom myself. At first, I thought that Canon's DPP software was good enough for what I wanted to do.... until I found out that Lightroom could easily do more (and in a very user friendly setup too). With one of the biggest differences, the ability to individually adjust separate color levels.
But don't be pressured into using RAW, if you don't really want to. Plus, the right PP techniques and software can REALLY turn JPEGS around.