There have been suggestions of matching up PvP pairings by score.
If you would like to play using certain rule sets (i.e. no upgrades, etc.) you can try playing the PvP Duel option. This allows you to play against a specific user, but no electrum or card spins are awarded.
There are also the Weekly Tournaments. Some of them have deck-building restrictions like no upgraded cards, or 30-card decks only. You could earn thousands of electrums, a Nymph, and bragging rights if you place in the top 4!