If you still have the s13 differential, there is no "bushings" to mount the diff to the chassis, the s13 differentials are just solid mounted w/ bolts.
If you have an s14 or z32 or j30 pumpkin, then yes, you can use those bushings. In fact you can even go solid bushing:
S14 240sx Solid Differential Bushings.
The s14 subframe has these nice gay bushings to let your diff jump all over the place..
While the S13's subframe doesnt have any stupid bushings where the diff mounts..
So if you use an S14 diff on an S13 subframe, the front mounting points may line up, and bolt up, but then ANY torque applied is going to be absorbed by the aluminum diff cover which is rigidly mounted to the subframe, not the bushings installed in the front mounting points, as designed.
doing it the other way has no "ill effects" because the cast iron diff is going to absorb all of the torque, while the rear mounting points on the aluminum diff cover are mounted in the S14 subframes bushings.
Hope this helps..