.25-06 vs .270 for mule deer? They'll likely never tell the difference. You could split the difference between the two rounds and buy a 6.5mmX.284 Norma. Cooper chambers the M52 in that round as well.
I can't really tell you what rifle to buy, but I will observe that I used to own a Sako 75 Hunter, and it was a good rifle but not as good as my Coopers are. My "go-to" center fire hunting rifle is a Cooper M52 Jackson Hunter in .280 Ackley Improved mounting a Swarovski 3-10X42. I don't really consider it to be all that heavy, but compared to a little wand of a mountain rifle I guess it is. At any rate it shoots tight little groups with most any ammo I load in the magazine, has a great trigger, comfortable well built stock, and operates more slickly than snot on a door knob. Cooper rifles in my experience usually end up being more than the sum of their parts alone, not that there are any bad parts; just that actual care is taken in mating them all together and making a product that works with the user to help you get the best results you can. In other words they are easy to shoot well.
Not just my isolated experience, I have two good friends that own Coopers (all .280's incidentally) and their rifles are both superbly accurate. I also own an M57 in .22LR and it is ridiculously accurate even with hyper velocity hunting ammo, I have yet to miss the head of a rabbit at any range I have taken a shot with that rifle (knocks on wood). Just about anyone that knows basic marksmanship principals that I have allowed to shoot either rifle has shot them both well. This leads to more of my friends ending up with Coopers, last one to shoot both of my rifles has one on order in 6.5mmX.284 Norma. I look forward to seeing what that one is like, M52 repeater with a 26" heavy bbl in a laminated varmint style stock.