I wouldn't choose either .308 or .25-06 for moose by choice even though both would no doubt do the job. Every caliber requires good bullet selection and shot placement. Come to think of it though, countless moose have been cleanly taken with 6.5x55 and .30-30 rifles over the years and I have shot one moose with each of those when helping someone else. (Both one shot kills.) If choosing either round, I would prefer heavy for caliber bullet weights (120 & 180 grains respectively) and have never had a bad experience with Nosler Partitions. Some of the more modern bullets may be preferred by many but I've always been happy with partitions as they shoot and put game down well. I consider both cartridges a bit light if you prefer "break em down" shot placement. If you avoid the point of the shoulder or raking shots and only take a reasonable shot at an unsuspecting animal, then moose are not hard to kill. If you get their adrenaline up, then you are in trouble no matter what you are carrying!
If travelling far or depending on factory ammunition, then I would give the nod to the .308 hands down as they are more readily available. Even with hand loads, I believe that I would prefer the .308 for moose and I have several friends that have used one for many years in Newfoundland. I know one hunter that used a .25-06 for caribou to great success and used it twice to take moose with no issues.
Families have been fed for years with much less capable rounds than either the .25-06 or .308. Be a patient and disciplined hunter, shoot straight and don't believe too much of what you read on the internet! For a dedicated moose rifle, I would suggest a .30-06, 9.3x62 or a .300 mag with good bullets for that little extra margine of error however you still have to shoot it well and consider its limitations.
