Well, in the BLR, the .358 is going to give you more energy, bigger bullets, and bigger holes, as well as let you shoot pistol bullets. The .308 is going to give you better bullet selection and better BC on your bullets. Personally I'd lean towards the .358 in the BLR as it's not a long range rifle anyway, and it seems the .358 has everything else going for it, besides high BC bullets.
The 8x57 thing gets more interesting. A handloaded 8mm mauser wil push 220 grain boattails fast enough to generate energy levels pretty close to a handloaded .358 (3000+ ft/lbs), and those 220's will carry their energy way out there and penetrate very well. The .358 can still go heavier on bullets, and make a bit bigger holes, at somewhat reduced range though. Slight edge to the .358 here in my books, as I've never had to shoot a moose at ranges where the 8x57 is going to really pull away from the .358 in terms of ballistics, and I like the big bigger bullet and shooting reduced load cast lead at grouse and rabbits.
All of these cartridges are very effective on moose anyways however.
