Who makes the best subwoofer for music? REL or JL AUDIO? REL uses High level, JL AUDIO low level with EQ. Which will be better for music. 
So interestingly enough, this is the exact dilemma that I have been having. I have been torn between the 2 brands for the same reason and have not been able to actually buy one over the other. What I find interesting, and maybe others can help explain, is the large power difference between the amps of the two brands. Yet both have great bass, just different style bass. 

I would not worry about the rated power and look at total DB output if using in a home theater application. For music who cares as you will not be at the limit.

I would guess you are seeing the difference between the efficiency of sealed vs passive radiator. The sealed box of the JL will require more power. Also keep in mind going from 800 watts to 1600 watts is only worth 3db and when not driven at the limit will not matter.
@jeffvegas --

I'd rid myself of brand-focus and gadgetry and go with the DIY-advice of poster @mijostyn above. Let physics have their say, and when you buy separate components (certainly electronics) reliability usually sees a clear boost. Cheaper as well.   

If DIY is a no-go I'd go with the likes of a duo or quartet of PSA's S1512. Very high quality subs with great pro drivers and good ICEpower amps - way cheaper than both REL and JL Audio to boot. 
Have *both* REL and Rythmik and have compared extensively, too. Both are good. Rythmik has no weak bass response or lack of dynamics in my room and no delay in the sound. Jim Salk, a top-notch speaker maker, uses Rythmiks in his custom subs.

Still, rooms are a big factor and of course so is subjective perception. Good luck with your REL and JL AUDIO comparison.