I'm a .270 guy. You give me a choice between .308 Win and .270 Win, and I'm grabbing the .270.
But, most importantly, I'm far more familiar with my .270 Win than any .308 available to me. I know that .270. We have history.
Take what you prefer. A rifle that you like and know is better than something you don't.
Ammo? I'm a big fan of 140 gr Partitions in .270 Win. 140 Ballistic Tips would be a close second. There are plenty of other good bullets, too. But the above are what I would use (and usually do).
This year, however, I had the barrel chopped and threaded on Ol' Reliable, and my "one load to rule them all" with the 140 gr Partition no longer shot well ... and I didn't have time to re-tune it. So, I ran factory Hornady American Whitetail 130 gr (Interlock). The bullet isn't as tough as a Partition, but it's still plenty good for a Muley and tougher than something like a Core-Lokt.
The ballistic coefficient of all of the above bullets are "poor" by modern standards, but they're still good enough for 500 yards.
One data point to ponder. It proves nothing, but may be worth thinking about:
I hit a doe antelope in the center of the chest at about 400 yards with that American Whitetail / 130 gr Interlock. The bullet penetrated about 30-32 inches, before stopping on the ball of the left hip. It went through hide, muscle, bone, heart, lung, a little bit of liver, shed the jacket somewhere in the guts (full of grass), and then the core burrowed its way through muscle to the hip. I believe the core would have exited, had it not hit the ball of the femur.
Yes, it's a single data point. But I've seen many similar (or better) performances with similar or 'weaker' bullets.
For Muleys, I'd still be willing to use Core-Lokts if it's all that I had available. The .270 Win 130 gr Core-Lokt (whether factory loaded or handloaded), in particular, has done very well for me in past years, and the same goes for many other people in my family. The 165 gr Core-Lokts (found in .308 Win and .30-06), however, seem far more fragile and have destroyed far too much meat for me to use them. I would NOT use a 165 gr Core-Lokt if I was using a .308.