I have a P/B and a B/B. The level 10 ability says "Hits an additional time if the user attacks first." It doesn't say the ability is dependent on being a faster breed. And unless you're either fighting something that has an ability that goes first (i.e. Surge), or you're going against another Flying pet, you will always go first.
To add, most of it's abilities are strong against Aquatic, so chances are, if you're using the pet properly, you will go first.
It seems to me then that P/B would be the way to go. And I don't see the point in hunting down a S/B. Though I may keep hunting for a rare P/B.
Any other thoughts?