Is it faster to jump constantly while sprinting, or just sprint? It seems to me that Jumping is faster but I'm not sure.
After doing some testing, I've found that jumping does not allow you to cover ground faster than sprinting.
To test this, I created two videos of the same character moving across a relatively level area just outside of Sanctuary - first by only sprinting and second by jumping repeatedly while sprinting. I started by backing my character against the save point near the Sanctuary entrance and pointing him toward the center of a large boulder in the distance. I then recorded 30 seconds of jumping/sprinting in a straight line (after having a few takes interrupted by Rakks, Bullymongs and bandits). Incidentally, the reason that the videos are that length is that I have the trial version of Fraps, which stops recording after exactly 30 seconds.
I then uploaded the videos to Youtube and used Youtubedoubler to compare the two. You can see that at the end of each video I'm at almost exactly the same place (right in front of some bullet holes and dead Bullymongs). The jumping looks like it's very slightly ahead, but I think that is due to the fact that I started moving a bit sooner in that video.
Jumping is recommended if you have any movement-enhancing kill skills, because if you jump while a kill skill is active, but it expires while you are still airborne, you maintain the same movement speed as when you left the ground. Jumping gets you around more quickly if you have movement-enhancing kill skills.