The lever action in .30-30 has been Americas Deer Rifle since 1894. Dropping down to a pistol cartridge is a significant loss of power and range. Even the .30-30 isn't known for much better than 250 yards, but that does cover most shots hunting in edge woodland.
The lever is ambidextrous, but is also old school - which means it takes some workarounds to get modern performance. Leverevolution ammo improves range and flattens the trajectory a bit, making the combination work further with "point blank" aiming. Less figuring holdover means less chance of a bad shot - or not getting one.
Having hunted with the Lever the last five years, it's light, handy, won't take a good scope mount, or has much option to put it exactly where you want. The loading cycle is arbitrary, and clearing the gun after hunting means jacking all the rounds thru the chamber. That's a chance for a ND every time right there, plus bangs up the bullets unnecessarily, which lessens accuracy.
They work ok, but having used the AR for 22 years in the Reserves, it's better.
The AR is inherently more accurate, and easier to get it that way. It's just as light and handy, the flattop scope rail puts it where it needs to be. Operating it is easy for lefties, and left hand models are available. Loading and unloading it is much simpler, safer, and easier. You have more choices in cartridges than the lever - BTW, Winchester is just a name for a high grade Japanese repro now, so only old levers or Marlins are your choice anymore. There's over two dozen AR makers of repute, and more models than you can count.
If you go AR for a hunting rifle, the better option is 6.8SPC, the #1 alternate selling cartridge. You get 40% more power, and avoid the kinky impractical magazine and low performance of the 7.62x39. A fixed stock flattop 16" barreled midlength gas makes a great deer rifle.