I've killed deer with both. The 223 was 580 Mini that loved the Sierra 65 grain SP and H4895; 2840 fps and three shot groups in 3/4 inch at 100 yards. Heart shot on a button buck at 160 yards with full penetration; he ran maybe 15 yards and dropped.
The 7.62×39mm is a great all around cartridge and we've used it for decades here. Even with imported soft points, a fully capable deer gun to 200 yards or a shade further. I can't remember how many deer we've killed with it but here are the two most recent from 2017.
My wife swatted the doe at about 220 yards with her CZ-527 using Barnaul Golden Bear SP. She clipped the spine at the shoulder with full penetration, doe went right down and kicked itself 10 feet before expiring, The buck I took with a WASR 10, running hard broadside at maybe 60; spined again, behind shoulder. He went down so hard he slid and never moved from where he stopped.
The AK shown with the buck has Tech Sights and a Power 'Red Star' adjustable trigger set for a two-stage, four pound crisp break. I've got a 200 yard range out the back door, so it's easy to tell what works and what doesn't.
Don't buy the line that imported steel case ammo is inaccurate. The CZ-527 will keep five Tula FMJ in three inches at 200 yards. The shortened/recrowned Yugo will give the CZ a run for its money. Imported soft point (I got a deal on a bunch of Barnaul 125 a few years ago) kills deer just fine. 223 if OK if applied with surgical precision on broadside shots. The x39 has better penetration and will allow you to take shots I would pass with a 223.