The hulls are essentially the same, but the cruiser does have more room and does have a slightly different layout.

I spent 5 1/5 years on DD970 (USS CARON) (A Spruance).

Back aft, where you would put a VLS system was where the NATO launcher was.  Internal configuration of DD963 class wasn't set up for MK41 there.  On KIDD class, MK 26 was designed in from the get go.  Something to remember about MK 26 is that it is a rotory magazine which stores the missiles vertically. Two mods of that launcher, one with one ring of missiles, one with two rings of missiles.  Back aft superstructure is wide enough for two rings as you can sort of rearrange placement of things back there.  Can't do that with MK 41.  Size is fixed at about 24' x 24'.  Also, VLS is configured to launch TLAMs and it (MK 41) is taller than MK 26.  MK 26 missile is about say 15 feet long more or less.  VLS missile cell is about 24 feet long.  MK41 would require much more internal rearrangement. CG-52 (First MK 41 CG) was significantly re-arranged especially back aft, even though the hull from main deck down is essentially the same layout.