I have owned several 22-250 rifles, and I really like the cartridge. I used to run aorund with a bunch of varmint shooters who shot 220 Swifts, 223s, 225s, 22-250s, and even a 224 Weatherby. The cute little rifle Weatherby used to chamber for that cartridge pretty much sold the cartridge, becasue if you were buying Weatherbys, you bought Weatherby cartridges (up until the late 1980s).
The cartridge itself is nothing to get worked up over, and it can be troublesome to reload because of the belt. If you really want one, go for it, but I would never pass up a 22-250 for a 224 Weatherby. Ammo is way more expensive, as others have pointed out.
I have seen several 224s over the years that had been reamed out to 22-250, so apparently those owners were not enamored of the cartridge. Also, please note that Weatherby no longer chambers for that cartridge.