While battlebots may or may not have more robots competing over the course of one year, let's consider the average lifespan of each battlebot.
Not very long
Let's say a battlebot somehow survives for a whole 3 months before it is killed by another robot. Now let's make an even more ludicrous assumption and say that all battlebots live for this long.
Thus, we can multiply the average lifespan of a robot to the number of robots to find out how many robots at any given time alive and having an influence in the world:
Battlebots: (0.25 years/robot)(500 robots) = 125
FIRST: (1 year/robot)(500 robots) = 500
Thus at any given time FIRST has 4 times as many functional robots in existance
This is just one way that FIRST is bigger. Look at the # of matches held per year. FIRST probably blows battlebots away. Look at # of people involved. Battlebots has many fewer people per team, so FIRST is bigger in that sense as well.
Patrick