These two calibers have been compared more and longer than possibly any other, certainly in varmint class. The funny thing is they are about as close as two calibers can be. they are like twin brothers, one of the working class one white collar, one some what savvy one "the varminter". . They are my two favorites, and as a 22-250 shooter I will give the gentleman's nod to the Swift. Many believe the Swift was first but both spawned around 1915 (the great wildcat era)as wildcats. Winchester simply mass produced the Swift before Browning did the 22-250 of which Remington later got credit for. Neither were developed by a factory. To me there is simply know better than either for varmints & predators from short to long distance. Why ? Because they shoot 50 - 60 grains fast & flat to 300 yards without hold over. 50 -60 grains has the smack I appreciate and is proven on varmints & predators. They are both inherently accurate shooting .5 is all to common. They are both more accurate at 300 yards than sub-calibers. They both have varmint / predator kill power at 500 yards.
Barrel life questions came from pre World War ll and grew with exaggeration over time. Using top quality barrels of today's modern corrosion resistant steel, sustained fire practice's, and proper cleaning it will not be a issue with either for the hunter rod & gun club type shooter. Both had good solid careers in Bench Rest until the 6mm' s came along. Both still do very well in Bench Rest Factory Varmint Class out to 300. Honestly I feel there is none better still today for varmints and predators. I also like the .223 but, why not have a rifle that shoots 55 grains flat ? 20 calibers are nothing new either. There wild cat days date back about the same as the 250 & swift but they don't carry the grains and results have been "so,so" on predators at a distance and even groundhogs to a lesser degree. They don't carry the smack of a 55 grain.
Personally, I believe you only need one varmint predator rifle if it's a 22-250 or 220 Swift. The only exception I can think of is a hot Prairie Dog town........then take one of each (grin) in heavy barrel. If you have one of either 22-250 or Swift, the rest of the Varmint/Predator Rifles are really just for collecting,talk,hype,fun,etc.
They do it all......
I don't use either for Deer. To me they were made for and shine at close to long range, varmint to predator,factory bench or field highly accurate, hot rods. That shoot the grains I prefer for such.
As has been said, either if you re-load or the Swift if for a more special feel. For factory ammo the 22-250.
If there ever was a pair of "brothers in arms"..........these two are it

:-)