Both are very good! I would go with a 7mm, it doesn't hurt to have a little better ballistics in the mountains. For me, it would come down to confidence for a one shot kill, money on the line type of thing. IMO.
Just an aspiring sheep hunter here... I just went through the same dilemma in preparation of doing a AK hunt in the next few years. I decided on a Boswell Ti-SLR in 6.5PRC w/ a 20" barrel.
Just hours before leaving for Alaska, Steve Speck shares the full gear list he is packing for his 10-day backpack Dall Sheep hunt. Steve is using the Exo Mtn Gear K3 3200 Pack System for this hunt and has a total pack weight of 43 pounds. Watch Steve go through every item in this
My first choice would be a the 6.5. I personally would look at the 6.5 prc or 6.5-284, both are very similar but have more power than the cm. The other cartridge I would consider is the 280ai. The recoil will be minimal in a lightweight rifle. You can also find factory ammo if you don’t reload.
I would highly recommend a chassis. Switched to HN26 chassis this year. Shoots great, but another thing I found is that a folding stock is very nice for shortening it up when you want to throw the rifle in a tent at night.
In my opinion, the caliber of your rifle is the least important thing on a sheep hunt in regards to killing a sheep. As already stated by others, sheep are not hard to kill and I believe the longest shot we’ve had to take on many rams killed is about 400 yds with most being way closer.
I say build a rifle that is exactly what you like, what you want to carry (weight and length), and that you can shoot well. The cartridge almost doesn’t matter except
ammo availability in a pinch is a good thing to consider.
If you could build your ultimate sheep gun what would you build? For me it would be. Remington or clone action 26in proof barrel 7wsm 1-8 twist Timney 517 trigger Manners carbon fiber stock one of the hunting flavors.
Super fun to geek out on this custom stuff- the furthest I got is a semi-custom Sako Finnlight 85 with a K.S. Customs 6.5CM barrel finished at 24”. Topped with a Swaro Z5 3-18x it made for a sweet rig and killed a couple bighorn and a pile of deer.
Then I realized that a stock T3 was just as accurate and a little bit lighter, lol.
Considering that you can actually find brass all over and avoid the PRC clickers I'd go with a 6.5-284.
Or straight 284
Or 6.5 Creedmoor but that'll do it too easily.