I find these two points to be contradictory. Generally speaking, battle levels with 2 carrots are quite slow paced, due to the fact that in a duel, a situation can arise where each player camps at a single carrot. Plus, if the level has more than a single route between the two carrots, the players can go back and forth without meeting each other. Look at battle 1 as a prime example: it is a very slow level where this can happen. Three carrots reduces the problem, but I find they have to respawn quickly for this to work. A lot of powerups also helps.

Levels with a lot of carrots (like say 4 or more) or quickly respawning carrots (10-15 secs) tend to be faster paced than levels with fewer carrots, despite the fact that players have more oppertunities to heal. The reason for this is the fact that a lot of carrots encourages a lot of movement between focal points in the level, creating highly dynamic gameplay where players are constantly exposed. An enemy must be chased/ambushed and attacked aggressively in a level like this, because simply hitting them and running away will mean they can heal quickly. The exercise of camping the single location of a carrot also becomes rather pointless. This, in my opinion, is the definition of fast gameplay. I should also say that strategy can still be a vital part of levels like this, but with more of a focus on quick thinking and situational tactics than in a level like battle 1.

I might make an entry to this contest, but no guarantees. Suffice to say, if I do make a submission I hope that it will not be judged poorly because of this.