Black Mesa, aside from just graphical and audio overhauls, also uses different (many would say tougher) enemy AIs, which significantly changes the sort of strategy which the player uses for encounters. Much of the game is also pretty significantly reworked, I believe On A Rail is much shorter and the Xen chapters are muuuuch longer and waaaay better. Black Mesa also adds more puzzles, making some use of the physics simulation of the Source game engine.

All in all, it’s the same story as Half Life, but a pretty significantly different experience.