Wilson Watch Dog or JL

I would suggest that the configuration is more important than the brand of the actual sub. To reduce the major problem of room modes, I would advise multiple subs. See here for an introduction to the argument: http://www.acousticfrontiers.com/20101029using-multiple-subwoofers-to-improve-bass-the-welti-devanti...
One way to do this would be to use the Audiokinesis Swarm system: http://www.theabsolutesound.com/articles/audiokinesis-swarm-subwoofer-system/
For even better results, you may want to add a DSpeaker Antimode 8033 dsp room eq system: http://www.theabsolutesound.com/articles/dspeaker-anti-mode-8033-dsp-subwoofer-equalizer-tas-204/

And of course you could just get another REL B1. Twin subs are almost as good as four. Of course, this too with room eq.

Yes thank you for the information.  I aware of the obvious advantages to duel subs and I also have significant room treatments as well as EQ, crossover, time delay, via McIntosh MX150 as well and ME220 room EQ. 
But for the consideration of this question, just comparing the "sound" and "tone" of these subs in question.  My experience is there are many subs out there today that will do just fine for HT.  As you mostly need power to move air being feed from the LFE of the processor.  However to have a "musical" sub for 2 ch that will augment the L-R is a bit more tricky.  Again anyone with experience comparing the Wilson sub to JL in their system.  Thank you

We have some of the same brands. While I haven't heard the Wilson sub, I can tell you that my dual JL Audio F112's mate seemlessly and are a great match with my Sophia 2's and Mac MC501's.

I'm very happy with JL subs combined with my Wilson speakers.  I think that you are better off with a specialized sub manufacturer but integration and crossover are key to getting good sound.  Wilson recommended that I run the mains full range but this made proper sub integration very difficult so I followed JL's approach and high pass filtered the mains with a better result.
You can see my system here: 

https://systems.audiogon.com/systems/5395