Hello,
Would both players get the same ninjas, or would players get two different sets of random ninjas?
Thanks!

Well, judging by how most arena training matches go, it seems like the winner would immediately be determined by who got the better ninjas, and the loser would just immediately quit, would it not?
Imagine a match up where someone gets a fairly balanced set with, say, Lee, Guy, and GNW tenten. And then the opponent gets Founder madara, and....anyone. There's virtually no situation where the second team loses. In the vast majority of situations there's going to be an immediate and obvious team imbalance and most players are going to quit. How do we address that and still keep it fun?

So the more you push this system, the closer and closer you get to....Zenith?

EDIT: To clarify, since I'm not sure it's super clear, there is already a codified "tier list" for ninjas: the point list used in zenith. So what you're describing is basically Zenith, but with a few extra and a few fewer steps. And on all the time.

That being the case, I can submit an "always on" zenith training mode suggestion for you.