I wonder if I can reprogram my 5.0 XK w/ CATS and flash the XKR module to stiffen up my ride,
or is springs the only difference?

 

You can try turning CATS off which will default it to the hardest setting, you could try different spring rates such as those from Spires OR you could do the best upgrade and go with fully adjustable coilovers such as BC Racing adjustable digressive shocks and custom spring rates.

 

Although mine is a 4.2 I have tried the xk, xkr and spires (eibach) springs.

There is a huge difference between all 3 springs in terms of comfort and handling and honesty I comes down to your driving style , if you drive the car hard I'd be going the spires as these are definitely the most hardcore of the lot (even firmer then the xkrs)

On a side note the BC racing adjustable coils weren't available when I upgraded my springs , had they been available I would have gone down that path as they are lighter, obviously fully adjustable including the ride height and most importantly save you the trouble of swapping out a shock when it goes faulty.