I would say the same, if you can afford two Rifles then, I would go for the .22 LR and the .223.
They are both perfectly capable, time proven rounds, indeed, the .223(5.56mm) is, in a slightly different form, what you are shooting out of your SA-. And the .22LR has killed more Rabbits and other vermin than is imaginable, the figure must be in the Billions.
You could always go for other calibres for fox such as the .22-250, .222, .22 Hornet or .243 but the .223 is used by so many fox shooters, there must be something good about it!
If you are really stuck for one rifle, then depend