As far as which round is better, I'd say it's easily the 7.62x54R. Ballistically it's only slightly superior, but as far as surplus ammo goes, there's a ton of it out there, much of it is good and nearly all of it is dirt cheap. It's not what you would use for deer hunting, but you can afford to go out and practice with it until your shoulder is black and blue and an M44 can do just that.
If you don't care about the availability of surplus, then I'd go with an Enfield. They have better sights, a faster action, lighter kick, a more convenient safety and are easier to mount a scope to. Both guns are capable of decent accuracy, but don't always deliver. The Enfields sometimes have worn bores. They were shot with corrosive ammo and may not always have been properly cleaned. Most of the current MN's on the other hand were rearsenaled prior to being put in storage and the barrels usually look very good. During the war years however, they didn't always seem to build them right and I've had a couple of 1943 Ishvesks that grouped worse than my Remington 870.
If you really want a nice Moisin Nagant, get an M39 Finn. You'll have to spend about $200 more, but you'll get a much more accurate and pleasant shooting rifle. M44's kick like mules and have a muzzle blast like a howitzer.