For what you have in mind I'd chose the Winchester 70 out of those two. Actually, I wouldn't chose either, and I'd get a nice Savage. However, if it's down to those two only I'd choose the Winchester.
That being said, I own a BAR in 30-06 and I will tell you why I wouldn't chose it. The first reason is this gun is very very picky on ammo accuracy wise. All of this shooting was at 100 yards. I was trying to shoot Winchester 150 grain Ballistic Silvertips in it and was getting about 6-8" groups. I couldn't figure out what was going on and why it would not hit the same spot. So I tried several other kinds of ammo. Remington Core Lokts in 165 grain (these shot huge groups too), Winchester Power Points in 150 grain (groups with these were smaller, but still pretty large), Winchester 150 grain Silvertips (Classic ones, shot a great group at 50 yards, but wouldn't group at 100 yards), Winchester Soft Points in 165 grain (grouped about like the 150 grain power points. Maybe 4-5" groups), Federal 150 grain Power Shok soft points (groups 3-4"), and finally Federal 150 grain Fusions (best I've found, 1.5-2" groups depending on the day).
As you can see I've tried a lot of different ammo and other than the Fusions I've not found any that grouped well. I can sometimes get groups about 1" with the Fusions, but more often than not they are closer to 2". The second best I've tried is the Federal Power Shoks which seem to group about 3" sometimes 4". The rest shot horrible.
I've done a lot of reading on this and while there are some reports of people saying theirs shoots sub moa, I see a lot more complaining of having issues like I am with 2-3" moa accuracy. Now this is fine for deer hunting at 100 yards, which is what I use it for. However, I'd think once you got out to 600 yards the groups would be horrible to the point where you probably couldn't even hit the coyote. That's just my guess though.
The only other issue I've had is the trigger is fairly heavy. I'd like it lighter, but from what I've read not many people work on them so I've never had someone try to fix this.
I really do like how the gun feels, the finish of it, it's reliability, and everything about the gun except for the accuracy. If you were shooting at 100 yards I wouldn't hesitate to recommend this rifle. Yet at 600 yards, I just don't think I'd want it.