My son-in-law-to-be has a .308 Ruger Scout Rifle. He couldn't give it to me. With composite (correction: LAMINATE) stock it is not light. Muzzle jump and blast are awful. Rough action. I hate that dinky scope mounted on the barrel.
I have no trouble acquiring animals quickly and accurately with my heavy WWII 30-06 Springfield with 3x9x40 Nikon.

2019: Gemsbuck shot twice on the run in thick cover. First in the chest through the heart incoming at fifteen yards. Second shot through the heart as it ran by at twelve yards.

2019: Muley buck shot on the run at 65 yards. Dropped dead. Hit him where the neck meets the shoulder.

2020: Fifty yards on the fly through the heart. Exactly where I expected the bullet to hit this coyote.

2021: Hartbeest shot a second time on the run at about seventy yards. Hit too far back. Fresh bedding shrank after rebarrel a few days earlier. I put the Springfield away after that. This was the only animal taken with my rifle of eleven that trip.

2021: Buffalo shot with borrowed CZ .375 with older 3x9 Leopold. First shot hit him on the run at 65 yards behind the shoulder almost quartering away. Both lungs shot out. Follow up shot in the chest as it was facing us ready to charge.

Learn to shoot moving targets at a shotgun range and you'll have no trouble taking running big game with a "normal" rifle. One thing you learn shooting trap and skeet is heavy guns swing better than light ones. One thing you learn from spending a lot of time at the range with a lightweight short barreled big game rifle ... how to flinch.