My son and I have been using TSX/TTSX bullets for the last two years out of his 25-06 (100 gr) and my 300WBY (180 gr). I find that the bullets kill very effectively and efficiently. In two years, only one of twelve deer required a second shot and that was because my first shot was off of my knee at 250 yards (the doe bedded down a few steps later and then I proned out and put one just behind the shoulder). I get plenty of bang-flops, but I tend to crowd the shoulder. I'd rather lose a little meat on an animal that's easy to find than spend all day looking for an animal because I couldn't stand to lose a pound of hamburger.
I have found that, especially out of the 25-06, the exit wound is smaller than I would like to see. It still kills plenty fine, but if I had to follow a wounded deer through any kind of thick brush there would likely be very little blood to follow.
I've seen deer hit through the ribs with both cup and core bullets and monos take off on a dead run. Fortunately, being in the prairies, I can usually watch them until they pile up anywhere from 100 to 300 yards later.
The two main reasons I use monos are 1. they shoot well (in my experience), and 2. I don't end up with lead shrapnel inside the animal. If a guy isn't at all concerned about the bits of lead, I see no reason to shoot monos unless they're the best shooters. I don't think I'd shoot monos out of anything smaller than the 25-06 (except perhaps the varmint versions), and certainly not out of anything with a muzzle velocity of less than 2900 fps.