I have had no problems using AAA NiMH rechargeable cells in my PBSF tail lights and they last for many hours when set in the flash mode. And since I use NiMH AA and AAA cells in lots of other devices (GPS, camera, flashlights) this has been more convenient than yet another type of proprietary battery. For a tail light which may not need charging for extended periods of time I'd recommend the Eneloop or equivalent 'pre-charged' Duracell type - they have a much lower self-discharge rate so they maintain their charge for many months when not being used.

OTOH, the Hotshot is much brighter than the PBSF (incl. the Turbo model) and would be a good addition to your PBSF. I'd keep both since there's always the possibility of a rear light failing and you might not even be aware of it immediately. Better to have two separate rear lights.