My first requirement is, it has to make the tree. Second it should be something capable of picking its way through holes in the branches, to the top of the tree, should the cat go high. On occasion you might have back off a bit to get a clear shot. We used a Ruger semi auto .44 carbine, and a 1-4x scope, with good results.
The one I'm looking at I screwed up. I made some classic mistakes, and threw in some of my own. Practiced all summer on the level at cat targets with my Model 29. Got good and cocky. Come race day, it was a bright day with snow on the ground making it very bright. My glasses were photo gray and turned as dark as they could, got sweaty and alternating between damp, and fogged. The cat treed in a dark hole, on a very steep angle. First shot held up way too much front sight. Total surprise I'm expecting four legs to the sky, dawns on me what I'd done, so I immediately over correct and break a front leg. Cat bails we start again. Being crippled the dogs did catch it on the ground. Post event analysis of the variety of wounds on the dogs, and the cat looked like the old Plott caught the cat going away literally bit the behind out of it, the black and tan backing the older dogs play came in face to face, and had both ears shredded for his trouble, the little pit bull got the back of the neck, and the cat got the worst of that. About the time I got there every body was regrouping for round 2. Not wanting any more vet bill than was already on the docket, and ****ed at myself I waded in determined not to miss I waded in stuck muzzle to rib cage and finished it. Cat was pretty well done by then, but adrenaline, and testosterone cocktails don't usually make for good decision making.
I'm not saying cats are tough, but technology can be a huge variable. I saw a factory .270 130 grain core loct fail to penetrate the shoulder of a medium sized male, and require another to finish it. Had I not been there and cleaned the animal I wouldn't have believed it. I don't believe we could make it happen again.