It is one of the older rounds that was touted for it's accuracy with certain loads. It is a higher velocity round than the .223 and thus is flatter shooting but others like the 220 Swift shoot flatter yet.
I shoot a 22-250 and sub 1/2" 100 yard groups out of my Savage 12BVSS are the norm using BVAC 55 grain ammo loaded with V-Max bullets. The other advantage is the 22-250 is relatively inexpensive compared to rounds like the 220 Swift.
The venerable 22-250 has seen it's day and was well thought of during it's time. Many varminters now consider the .204 superior in accuracy and barrel life. That said, the 22-250 is still a good round.
The 22-250 is an old school round, but a good one. Ive shot them in the past with great results. An a fairly reasonable price on factory ammo, and easy to find at most shops.
I own both in 4 different guns..... 22-250 Remington police, 22-250 how axiom, 204 Remington sps, and a .204 reminton Vtr. The 2 22-250s are slightly more accurate out of a vice.....