The .308 for white tail is a good choice.
As to the Axis, I own one and am not one to recommend it.
Disliked its stock design. Caused my scope horizontal crosshair to move up to one inch on a 100 yd target. Have a 24 power scope on the rifle and easy to note crosshair movement on a 100 yd target. Just pressure on trigger when pulling it caused stock to flex when shooting from a benchrest. It was not me, not my benchrest. Had other gents take rifle to their bench to shoot from their rests and they noticed the crosshair move on target while pulling trigger. Stock will flex at wrist in area where rear of trigger guard butts against stock. I solved my stock flex problem by cutting out the receiver portion of the stock, flattening its sides and building a wooden stock around it. Altered the trigger guard piece to reuse it as it is needed to hold the magazine in place.
Trigger pull. Factory trigger leaves alot to be desired. Figured mine was around 7 lbs. Oh, its easy to do a trigger job on it and get it down to a 2 1/2-3 Lb trigger, which I did. Or you can buy a replacement trigger for it.
Spacing between scope mounts are wide. Be prepared to put a long scope on it, or buy extention rings/mounts.
On my particular Axis, have a rather poor ejection of fired brass. I need to yank back hard on bolt to get brass to dribble out of receiver. Unlike my two Stevens 200s, I can't slowly pull back on bolt and expect it to partially eject enough for me to grab brass. Brass will fall inside receiver.
Rifle does shoot fairly accurately for me. Own a couple of Marlin X rifles, prefer them over the Axis.