All the cartridges are quite accurate. The .223 is cheaper to shoot, whether you reload or buy factory ammo. But, it is 600 to 800 feet/sec slower than the .220 Swift or the .22-250. Those would be better at longer ranges.
I've shot both the "Big Boys" quite a bit. The difference is negligible. I've gotten equal-sized groups, down around 3/8" or so, with the occasional 1/4" (100-yard; five-shot).
I never had problems with case-stretch on the Swift. The .22-250 is allegedly more accurate if you use lower-velocity loads; I don't know; I've read otherwise.
I'll let others compare the Browning vs the Ruger, but I think I'd get the Ruger and then look for a single-set trigger for it. Or use the difference in $ for a higher-grade scope than you had maybe been considering.
Have fun!
Art