I think it's going to be a bit... Stupid. You already have limited use of Earthquake / Surf, etc. in double battles, but when you bring a third member in, you basically have to rely on attacks that single out the foes or attack them all at once. If you choose to attack them all, then your attack's power would probably be reduced greatly (like how in double battles, hitting two foes at once means your attack strength is 75% of normal -- I'm expecting something along the lines of 50% or less for triples).
What it will go into then is what double battle ends up being a lot of the time -- you single out a foe and take them out ASAP using one-target moves, depending on your type advantages... Only in triple battles, you can cover every type possible since you have so many Pokemon out already, so only the fastest Pokemon can win, really.
Finally, the last thing I'm worrying about is that your party can be severely crippled by losing even one member... And in-game, if you're in a tight situation, you'll most likely lose a triple battle anyway.