Jesse,
I have JPoints, Delta Points, one C-More STS and a Trijicom RMR 06. On a hunting gun, batteries are a total non-issue. On any of the newer models, change the batteries on a set interval. Depending on the specific sight, you can turn it off, set it down or use the supplied hood to lengthen run time. I do not fret batteries any longer. It's taken a few years of testing to get my mind at ease, but I am there.
As to the RMR Dual v. Constant dot (battery) the reviews I have read stated that there are times that the fiber optic is not quite bright enough, and it is not quite dark enough to see the tritium. Think, early morning, late afternoon/evening, changing timbered/blind hunting conditions (or dynamic indoor lighting when in defense mode). Hence my decision to go RMR 06.
Pop on over to Gabe Saurez's Warrior Talk Forum and in the optics section you can read a ton about RMR's.
Craig