The story, controls, or core gameplay mechanics have remained the same, however there have been various changes in other areas
Silent Hill 2
New voice acting, with the choice to use the original voices.
Comparison video:
A lot of the fog has been removed from the town, which was resulted in negative feedback from the original director of the first three games (source).
Comparison Screen shots:

Fog Horn removed from a scene:
Silent Hill 3
Both Games
The PS3 version experiences occasional slow down.
Finally, here is a video comparison of both games. The graphics in the HD collection seem a little more polished, but I personally don't see a huge difference: