My friend has a hunting partner that has used a .308 for moose hunting the last 30 years! It will definately do the job.!
I would just highly recommend using one of the Premium bullets, you'll get better penetration on a big bodied moose. I would also use a 180 grn bullet, such as Nosler Partition, Barnes X, Trophy Bonded Bear Claw, Swift A-frame. I know that you can get the the 180 grn Nosler Partition in factory ammo in Federal's Premium line! This is what my wife carries in her .308 for hunting up here in Alaska!
Good Hunting!
Del