For a varmit rifle, I'd take the 22-250. The 25-06 works great but I see it more as a hunting cartridge. You could make whatever you want into a varmit rifle, I used a 338 win mag years ago. It was a hoot but a day with it sored ya up some. As you know I use a 243 now and I like it.
.22-250 or the .25-06. opinions on which is better? Would be for an all around varmit rifle.
Of the 2 you mentioned the .22/250 would be best - the key words are "all around". The .25/06 is a great cross over cartridge when deer are on the menu. Ditto on what ChesterGolf said about the .243, one my all time favorites.
As I sit and glass, which is common for hunters out west, I have sort of quickly discovered something I never learned when I was younger.
In my youth I had enthusiasm and spirit. In my middle to advancing years I have creaky knees, arthritis, and I tire more easily than I used to. Where I used to sit on the cold hard ground I now look for that soft spot to sooth my tired muscles. That leads me to my tip.
Carry your soft spot with you!
In my pack I carry an air filled, ultralight, camping pad....