A few important questions to ask yourself before you decide.
1 Are you looking at factory rifles or having one built?
2 Do you reload, willing to reload?
3 Is this a dedicated predator/varmint rifle?
I've used 223rem and 243win for the majority of my life in my part of the country longest shots usually no more than 400yd. A 243win with 75-90gr bullets will be fine for either dogs or yotes out to those ranges. Factory ammo is everywhere and well priced as well. You can step up to 22-250 or even 25-06 and have more velocity and energy with the lighter weight bullets as well, no shortage of ammo for it either. 220swift is a heck of a round for them as well, factory ammo is a little harder to come by though. If you are willing to hand load any of the above would be hard to beat. I personally love the 243win it was the first high powered rifle I ever owned and I've killed many many a ground hog and yote with it, deer as well. Light recoiling not over the top on muzzle blast or high priced to shoot, I've shot targets to around 600yd with great result as well. It's been around for long enough reloading data is everywhere and many ppl are using it in long range competition and tactical shooting for the reasons above. I'm not a huge fan of all the new wiz-bang magnums out there, for me a rifle with ammo everywhere and that's accurate is where it's at.