As far as I kniw, there should be nothing wrong with swapping the ring and pinion - other than the fact that you can possibly swap the whole assembly without a problem.
The main differences would possibly be:
1. some rear diffs are equipped with Antilock - but you don't have to use it if your vehicle does not have Antilock. The reverse may not be true...
2. some front diffs may have a steel case - which you definitely want to use!
3. some front difs may have different spline counts on the side gears from those found on youe axleshafts.
Because of this, it would be very safe to just swap the ring and pinions as they are al identical. The downside is that you must set up the gears properly and, if you can afford it, do a complete rebuild with new bearings. You will DEFINITELY need a new crush sleeve - the old one may not survive the diassembly/assembly process. If it does not, you will start toget unwanted pinion gear motion.
I hope that this helps!