Is your .243 a heavy barrel?
What do you hunt with it?
What do you want to hunt with a new rifle/caliber setup?
I'll do some guessing here.
If you are considering a .22 of any persuasion and you already own a 6mm class ..... you are not wanting to cross over from PD's to big game with it.
So lets just consider varmints and predators.
I have used the .243 in three different rifles and consider it to be one of the finest "Dead Right There" (DRT) cartridges available.
Yes, I have a .25-06 too ..... and it's the very best knockem down .... period.
But there is a price ..... more recoil. Mine is a big long bull barrel and it's a pussy cat but it's no easy packer.
So for the kick ...... the .243 really delivers.
BUT it's over powered for PD's or squirrels etc.
Now the .22-250 ...... I have used it very extensively too.
It's a GRAND cartridge ......... but the .243 does coyotes with substaintally more authority!
My varmint rifles are really coyote rifles used on smaller game just to keep my edge ...... and right now my day in and day out coyote rifle is a .223 rem. My .22-250 had just died ..... needs a new barrel .... and I wanted a very easy packing cougar rifle .... the CZ 527 American got the nod in .223 rem. but I miss the .22-250 on really long shots.
IF I wanted a squirrel gun for some coyote work ... I'd go with a .223 rem.
IF I wanted a dedicated take no prisoners coyote rifle the .22-250 would be a MUCH better choice ...... BUT you already have a .243 ....... and THAT is tops!
With a .22 anything ...... you'll have to test bullets ....... with a .243 ..... it just plain does coyotes RIGHT ....... with most ANY SLUG!!! When I started with my .22-250, I had a bunch of run offs. My first good dog slug was the Sierra 55 gr. Game King, a spitzer. Then I switched to the Nosler 55 ballistic tip and the dogs dropped like FLIES!! ..... even past "300".
Poooooor coyotes ........ nobody loves them .......
My best advice is to consider a .223 if you are yearning the smaller critters since your .243 covers "dogs" very well at todays fur prices (near zero). Less powder burned and cheaper brass! If your .243 is a sporter barrel and you are looking for smaller groups .... then a bull barreled .22-250 would be nice mainly for coyotes ..... you will heat it up much faster on PD's or squirrels than a .223 though .......
........... sometimes we get antsy waiting for the barrel to cool on a warm day!!!!
OR you could end up like me ........ go crazy and have one or more of each ..... and still look for another combo!!!
I'll get flack for this:
Consider this as a yard stick ..........
For coyotes I'd rank the .223 as a 250'er ...... the .22-250 as a fat 300 ..... the .243 a fatter 300 but more smack down .... I did a coyote at 450 and it freight trained him! And the KING .... the .25-06 at nearly 500.
Three 44s