Apparently Mythbusters got to this 'can you fell a tree with a machine gun?' thing a while ago. They determined that yes, you could, in 45 seconds.
So that's 2,250 rounds, which at $0.50 a round is $1,125 for the tree.
Looks to me like it takes about three .50 BMG hits to knock down that tree in the clip below. Now, BMG is a little more expensive -- about $3 a round -- but that still works out to $9 for the takedown. If it takes four or five hits, it's affordable.
Sounds to me like there's no choice but to prefer the .50 BMG rifle for lumberjack work.