Ive got both as well and like them equally. Got the .223 first and it makes an excellent varmint gun and even a decent deer rifle. Ive shot everything from squirrels to deer from 50-350 yds with it and love it.
Got a .243 bolt gun last year as well as a handi rifle with a youth stock for my wife. Liked her handi so much I traded my bolt gun in on a new heavy barrel handi for me. One thing I like about the .243 is that its a better dual purpose gun. Takes down deer much better and still works for the larger varmints.
As far as accuracy with the .243 goes, my wife's shoots 1/2" 100yd groups un-modified. I haven't shot mine a whole lot but I bet its real close. Good enough to regularly smoke crows at 200+ yds.
My advice, get both. You'll be much happier in the end.