I have taken several deer with the 243 and 257 roberts. The 120 gr Partition in the 257 gave great results. The 100 gr Hornady btsp gave essentially equal results in the 243.
You should expect the 25-06 120 gr partition to be on par with the 257 roberts in terminal performance.
I think where you hit the animal has everything to do with meat damage. I hunt thick woods and prefer to take out at least one of the front shoulders. It doesn't matter which bullet you use, if you hit a shoulder, you relegated whats left of it to sausage status. That's fine with me though. I use the front shoulder for sausage anyhow. Deer in my neck of the woods are smallish. I don't bother with the ribs unless I get a big deer, so a couple blood shot ribs are inconsequential.
Right now, if faced with your choices, I think I would opt for a lightweight 243 for a woods/tree stand rifle or if my hunting was less walking and more "box" stand, I would get go with a standard weight 25-06. If I used factory ammo it would be Nosler Partition. If I handloaded I would load Nosler Partition. I am a premium bullet fan in sub 30 caliber.
My experience shows me that there is nothing marginal about the 243. 6 deer shot at, 6 deer hit where I aimed, 6 bullets performed as designed, 6 deer became groceries. One was shot with a 55 gr varmint bullet at about 400 yards. He did a 100 yard death dash and piled up. Note, my friend took this shot, so don't raise cain with me about a stunt shot. Two of the deer were big bodied SCI minimum blacktails at 250 yards. One took two steps and gave it up, the other took about 10 steps.
I would like to repeat that with proper bullets and shot placement the 243 is not marginal it nears perfect. The same can be said for the various 257's, but I consider them the perfect deer calibers with 120 gr premium bullets.
Bottom line is you cant make a bad choice with either of the ones you are considering. Hope this helps.
Paul