I played my 360 on a 11" SDTV and it looked horrible.
Then on a 18" PC monitor in full HD and it looked so much better.
Then when I got my PS3 I hooked it up on my mom's 50" SDTV because that PC monitor I mentioned before didn't support HDCP and it looked average (guess the screen was too big this time)
Now with my 24" PC monitor it looks fantastic.
So the picture of your TV should at least be better than in the SDTVs I used before.
But HD is definitely worth the jump.