Not sure about those games in particular, but usually the difference is in the music or cinematics. For example, Flashback CD was exactly the same game, but with rendered movies, instead of those clever shaded vector graphic real-time flicks on the cart. I think the music was "CD quality" too...
Eternal Champions is definatley not the same game. Been awhile since I played it, but it had a shitload of new characters that can be unlocked, a new combo system, new special moves, improved graphics, FMV, and much better sound than the cart game. Actually I didn`t like the cart at all, but thought the Sega CD version was very good.
I haven`t played the Shadowrun Genesis cart, and hardly played the Mega CD version, but I`m pretty sure the games are completely different.
Yeah, Shadowrun on Genesis is completely different from the Mega CD game. MCD Shadowrun is in jap so I didn't get far at all, but from what I did see it appears to be a picture+text adventure like Phantasy Star Adventure. I dunno if there are action levels or whatever, I didn't get very far since I was randomly choosing options and seeing the characters speak in gibberish to each other.
Eternal Champions CD is basically just an improved release of the game, not really a sequel but still much improved. It's the only SCD game I know of to use 256 colors simultaneously in-game (heavy use of hold and modify technique).