Full range or subwoofer with bookshelfs for best bass at low to moderate volume?

Thank you for all the good responses. As you can see from my original post, this is a modestly priced system as will be the subwoofer. If full range speakers were superior they would have been down the road sometime. My aging subwoofer was producing less and less bass at lower listening levels which prompted my original question.

In answer to Noble 100, my budget is $700 with shipping for the sub. A used one is fine within a couple of years old. This is a 2 channel music system. I have a fully finished walk out basement that is my "Man Cave", so I do not have any limitations by my wife for this room. It is L shaped. The larger portion of the L is 11 x 23 with speakers on the long side firing across the short side. Ceiling height is 8 feet. The other portion of the L is 9 x 11 with a 7 foot ceiling, and while it may add volume, I do not consider this a part of the listening area. Floors are carpeted and wall finish is drywall.

Willland, thanks for the offer. The subs you listed are older and I am not looking for anything over 3 years old. 
Bob_reynolds and yogiboy, I was surprised and happy to see the good reviews on the SVS subs, hard to find a decent sounding sub under the $1000 list price. I really wanted something other than black, but may consider black at a later date.
Thanks for the replies.

mtloriginal

Phasecorrect brings up an interesting point about the importance of set up as have others in this thread. In reading a review of the Elaq Debut  S12 EQ the reviewer came to the conclusion that it sounded better in his room than similar price subs that went lower and had more output, due to the built in EQ. So is it possible to spend a lot of time experimenting with placement and manual adjustments and equal the quality of sound of a sub with EQ? Other than the Elaq I have not seen other subs with EQ in my price range.