Doorknob posted the following statistics on Chat, which I understand are based on answers to existing challenges. All credit goes to him. They certainly agree what I would have imagined.
golfscript is shorter than pyth 6 times (~13.043%)
golfscript is shorter than cjam 16 times (~20.513%)
pyth is shorter than golfscript 39 times (~84.783%)
pyth is shorter than cjam 59 times (~60.204%)
cjam is shorter than golfscript 57 times (~73.077%)
cjam is shorter than pyth 31 times (~31.633%)
I was going to leave these to Doorknob to post, but I found them interesting and thought if the question is going to stay open a while longer, it would be nice to post them for posterity, before it gets closed.
Obviously the best language will depend on each specific challenge, and this data only considers the corpus of challenges that we have at the moment. A change in the type of challenges would alter the balance between the languages.
Additionally, this data reflects the state of the languages today (Aug 2015). The languages are still in development, so it will be interesting to see how they perform in later versions.
This only covers challenges where at least two of the languages participated, which is probably fairer than considering all challenges. Nevertheless, as in virtually any statistical analysis, it is arguable that there could be some selection bias. It's possible that many challenges were so suited to a particular language that the others were not even considered.