are you leaking from the battery on the one thats bad ? I dont' know off hand why one battery would be prone to issues and not the other...all things equal, but all things may not be equal is your battery is leaking fluid ..
do you have all your bolts tight, and everything torqued that should be?
what are the symptoms of the vibrations, does it happen at certain speeds or all the time, does if flucuate, does it change with rpm or speed, doe it go away when the brakes are applied,.
the sping based suspension...
doubt its related to the pinion angle ... I have OME heavy / heavy on my truck... no issues with pinion angle or caster. You very well may have a problem but I doubt its related to the the install on the lift.
Give a better description of the vibration issue and you might get some good...