It isn't just the power of the saw and bar length that determines what size logs can be milled. The distance between the vertical posts on an Alaskan mill only allow that which will fit between them. There are different sized mills. I don't know if the current mills come with the supplementary oil tank that drips onto the chain from above, my Sperber doesn't have it, but even with saws that have good oil output, my opinion is that the additional oil helps, although a slight hassle to keep shutting on and off the flow when running and stopping. The hot chain really can get a lot of crud building up on it. Not sure that in itself hinders cutting so much, but the additional lubrication is a plus.
I've milled extensively with 076s, single and double power heads attached. Unless doing dinky stuff, I wouldn't want anything much less in the power department. Power is where it's at, without it the going is just too slow. I've also milled with the 090 and 090G. Might want to run a little richer when milling, full throttle(s) all the way through the pass. The engines run hot.