I don't have a 243 Win anymore. But I've used it for years on deer with great success. And loaded with the 75 gr bullets it should be a great varmint round. I've also never shot a 243 WSSM but from what I've heard it is rough chambering a round from the magazine due to ist sharp shoulder. But again that is only what I've read and not from experience. In your case however, this wouldn't be a problem in a dog town.
IMO - I'd go with the old std 243.