Remington BDL stocks fit me very well.
The OP asks about a synth ADL. Yup.........same dims but maybe lighter overall by a few ounces. Big deal.
It will have a newer style recoil pad.
The old BDL's from the 70's had a good pad. I think the newer materials of the ADL synth pad to be better.
And that's just a newer style standard pad, not one of the even more new "trick" elastomer types.
It should have some muzzle rise and a bit quick to move the shoulder, but entirely manageable.
I had a 7 mag. Grew up being a varminter, went to a new coworkers house and he had a range out back. Handed me a BDL in 7 mag (1976 vintage) with a 12X fixed Leupold (was load testing). Asked me to shoot a steel plate at 135 yards, off hand, dead of winter. I did on the 3rd pass. He laughed, asked me to do it again, and I did. The plate was suspended from a wire. We checked and the 160 grainers had knocked dents in the plate to where there was a split at each impact (old RR track plate painted white).
Yup, I bought that rifle.
Sold it though, to get a .300 magnum.
IMHO the 7 mag was substantially more comfy to shoot, even with 160's as fast as you could push 'em. .300 mag w 180's is another notch or two above.
If I see a deal on a pre cerberus 7 mag ADL.........I'll buy it. Be my do all elk, muley and WT rig.