Yeah I'm sure the Yak-3 can outturn the La-7. Also, the La-7 I believe had a Ash-82FN engine, where the La-5FN had just a M-82FN engine, so the recoil would have been dumbed down by the heavier engine. But if they both have the same gun armament.
Then I'm going to fly a few sorties with the Yak-3 tonight and see how I fare.