Turn on your FPS display in your graphics plugin. Does it still hover around 60 (50 if you're in PAL land) or does it drop when you get to the second level?
Make sure you have FPS limiting turned on and set to 60 (or 50 for PAL).
How powerful is your CPU and your graphics card?
ePSXe 1.6.0 is known to have timing issues with some games. WipEout 1, for instance, has slowdowns in some areas of the tracks when running in it. If your FPS number stays steady but you're seeing slowdowns anyway, you might want to try sssPSX.