I loved the original and this is also up to par. If I could only make one suggestion for this kind of game in the future (a game that is separated into stages), it would be this: make the restart button (R) and instant respawn with no excessive wait time or unnecessary count down.
Don't get me wrong, the count down at the beginning of each level is fine, but making the level reset button instantaneous would really cut down on the frustration inherent in all platforming games. That being said, the controls are great and the levels are fairly times I.E: not impossible.
Great Work, I can't wait to see your future works.