That's a great question, and one I haven't considered before.
Some thoughts:
(1) Facing a bishop pair is much scarier than facing a bishop and knight, because it means every square can potentially be attacked from range, whereas if your opponent only has one bishop you can safely park your king on a square of the opposite color. So in this case the second bishop seems better than a knight.
(2) Knights are better than bishops against queens. If your opponent still has a queen, and especially if you are down material and need to come back, it's probably easier to do that with a knight than with a bishop.
Overall, I think if I had to play a game without a bishop or a knight (whether I was playing against an opponent who was also playing without a piece of their choice, or not), I think my order of preference would be giving up my c1 bishop first, then my d1 bishop, then my b1 knight first, and finally my g1 knight. But it's a close call.
with knights you get long sightlines and can use that to your advantage but often pawns get in the way. they can set up attacks and traps at any range. with knights you dont get much informational value but get surprise attacks seeing as no piece can spot them if they can be attacked by the knight. they are very good for scouting a specific square to see if theres a queen or other peice there. the movement makes them very hard to predict but at the same time can put them into trouble. (save for a knight vs a knight obviously)
would love to hear your opinions about this. personally i think that knights are worth slightly more when used properly but im only very good at the variant and by no means a master