A full frame sensor gathers 1.6x1.6 = 2.56X as much light as a Canon cropper. If you have the focal length available to frame the shot in the same way then you should see about 1 stop of improvement in noise performance. That can be important at higher ISOs or if you want to print/display at large sizes.
Apart from that the other value add is to potentially create shallower DOF if that's your aim, good for portraits and sports, not so good for everything.
If you want equal DOF for the same framing, which requires a longer focal length, you will need to stop down by a factor of 1.6X, which is almost 1.3 stops. e.g. where you might shoot with your 7D at 100mm and f/2.8 you would need to shoot at 160mm and f/4.5 for the same framing and DOF on a 5D or 5D2. If you stop down you'll have to drop your shutter speed or increase your ISO in order to maintain an equivalent exposure. If you can drop your shutter speed then you maintain the IQ advantage. If you increase your ISO instead you've just thrown away the noise advantage the larger sensor gave you. That's the theory at least.
There are other considerations too. The larger sensor tests the edge and corner performance of your lenses. You may (will) see increased vignetting, and may wish to apply lens corrections using LPIC in camera or through software. On the plus side the larger format means you enlarge the image less in order to produce your final print/display. That means that images can appear sharper. Errors like misfocus or poor lens IQ can be masked. Stopping down the lens for equivalent DOF can also improve lens performance, if you can reduce shutter speed.
Whether any of that is of value to you is something only you can say. If you want a play then maybe buy secondhand. You could always resell at little or no loss if you do that. If the interest is really more about full frame vs crop then a 5D should satisfy your curiosity. Of course the 5D2 adds video, AF microadjustment, sensor cleaning, a better screen and preview image, better battery life, better high ISO better build and maybe some other things too, but the choice is yours, not mine.
EDIT : What sort of subject most interests you for full frame? Maybe I can shoot an representative image with my 7D and 5D2 and send you the files for comparison.
EDIT 2: Oh, and of course the 5D2 adds many more megapixels over the 5D. The fact that I forgot to even mention that initially probably says something about just how (un)important they can be. People who take pictures rather than pixels probably don't much care. If they did then Nikon would be having a poor time of it with their D3, D3s and D700. I hear they're doing OK.
Still, having 21MP files to process is a great excuse to upgrade your computer.
