Does a downloaded game run slower than a physical game?

Loading from an SD card versus a cartridge may affect the game's load time, the actual framerate should be consistent once the game is loaded into memory.

Having said that, SD cards are Flash memory and are relatively fast, so you shouldn't see an appreciable difference in load time either.

While this answer was based on my experience, comments on Reddit seem to imply the speeds are roughly the same or slightly faster if you're using a better SD card.