FOR many years the .220 Swift had the advantage over the .22-250, because the Swift was a factory loaded round, while the .22-250 was a wildcat.
The Swift was king of velocity, BUT it came at the cost of a fairly short barrel life. Modern steels and powders have changed this quite a bit, but either round is hard on barrel throats when loaded to the max.
With Remington making the .22-250 a factory round, the advantages of the Swift mostly went away. The .22-250 uses the same standard head size as dozens of other rounds (.473) so the shellholder for the .30-06 or the .45 ACP works for reloading it. The Swift needs a shell holder for the Swift (or the obsolete 6mm Lee Navy, which was the parent case for the Swift)
If you are desperate, .22-250 brass can be made from the .250 Savage, or even, with the right forming dies, the .30-06 (although that's a lot of work), and since its a factory round for over 40 years now, .22-250 brass is common.
Swift and .22-250 barrels often have the same twist, 1-12 or 1-14, or they did before the fast twist barrels found in ARs today have proven the value of extra heavy (70gr+) bullets in .22 cal.
I've had a .22-250 since the early 1970s, and as far as I'm concerned, even though you might get a handful more fps with the Swift, the .22-250 is the king of centerfire .22s.