shooting sports (softball) and continuous shooting

Considering the Nikon P510 of the Sony HX200V for shooting softball games.  Need good battery life (often 3 games in 1 day).  Need good continuous shooting.  Need lens able to fit in hole of fence.   My current Sony (severy years old) does all this for me,  Either of these cameras seem to meet my needs; however the Sony is faster.  What I do not like is the 10 shot max on the burst mode.  Current Sony shoots slower, but continuous until you release the shutter button.

 I can get the Nikonfor about $50 to $100 less than the Sony right now, but I'm leaning toward the Sony.  Any thoughts out there?

Thanks