More wolves are killed with a .22 rimfire than any other cartridge in this country (trapping), I've put down many myself that way (.22 Mag). Next up for the title is certainly the .223, which is what the heli culls in BC and Alberta are done with, with cheap HPs or SPs 45-50gr, hundreds can go down to that in a winter.
While a wolf in a snare being put down is a different deal than a running 250 yard shot, I've determined after much experimentation they are not nearly as tough as they are given credit for. My theory is they're also not nearly as big as people think, this is a coworker's father off his trap line this winter, and is... a 110lb dog. I've found them to be thin skinned and as mentioned pretty easy to kill, and those were according to research I read years ago the heaviest wolves in the country on average (Wood Bison preying).
My thinking is many would shake their heads at selecting a .30-06 for 110lb deer... and wolves are no tougher. More tenacious, sure, they'll go a long ways on their front legs only if spined and so forth, but they die just as easily as the 110lb deer when hit right. In the same breath I absolutely will not criticise someone for using too much gun! There really is no such thing as we've discussed here at length, I've shot them with a .375 H&H. However you're not going to see any real improvement in effectiveness over the humble little .223. I'd love to see scale pics of 150lb+ wolves... But even at 150lbs, that is WELL within the .223's realm.