Hey

At the moment, it's not possible to have a track record of the opponents you've faced.
Only during the match itself, and if the player has typed in Battle Chat that you can check gear stats, etc. However, it's completely wiped upon refreshing.

As I said, though, right now it's not possible due to new programming and server storage. But who knows for the future.

That's unfortunate.
I'll suggest saying Hey in the battle chat to scout the player you're facing if it helps you understand certain gear they have.