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

I have an older subwoofer with bookshelf speakers and the subwoofer is dying. I listen mostly at low to moderate volume and am in the middle of changing over my system as my Pioneer Elite VSX 49 TXI receiver was degrading, also due to age. My question is whether a subwoofer with bookshelf speakers or full range speakers produce more bass at low to moderate volume? 

Current system:
Moon Audio 250i integrated amp
Angstrom signature 3 speakers ( 6.5", Seas drivers, 86 DB, 6 Ohm)
Paradigm subwoofer (needs to be replaced)
Denon 2910 used as transport
Looking for an analog sounding dac at this time

I'm running Revel M106 mains and an SVS SB16-Ultra sub. If you get a sub like the SB16-Ultra, there will be NO SPEAKER that comes close in terms of bass distortion or quantity. These subs also have 3 parametric EQ bands to deal with standing wave issues.

If you dial in the sub, it's pretty hard to tell it's there. For now, I'm really happy with the sound. I will have to spend a LOT on different speakers to achieve a significant upgrade.

The main issue I see with buying bookshelf or 2-way speakers is that you have one 6 inch driver trying to handle over 5 octaves of music. It means the lower bass from the driver will have high distortion and not much punch, and the higher midrange is being produced by a larger than optimal driver. In addition, it might be trying to reproduce 1500hz while trying to reproduce 50hz at the same time, and that causes phase distortion for the higher frequency. In other words, the 1500hz isn't coming from a single distance driver from you, that driver could be moving in and out a half inch or more.

I like the concept of the KEF Ref 1, because it has a modest bass driver to take the load off of the midrange driver. I would expect a better midrange from a system like that, and imagine they might be able to cross the tweeter over at a higher, easier frequency.

BTW, I replaced an old sub with the SVS and it is a huge difference. It really sounds integrated now and doesn't sound like it's behind.
I opted for the full range approach, albeit in a large monitor form. The main proponent being cost. An entry level musical sub will be 1-2k, an added cost I wanted to avoid. Plus subs are finicky: placement, crossover, gain. Always go the path of least resistance. Simplicity reigns.
Another factor: room + musical tastes. If I gravitated towards electronic, dub,etc the sub angle would be more attractive. However, no sub at all beats one that is improperly set up. So I went low risk, high reward.
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.
near full range speakers (40 hz or so) with a quality , higher powered amplifier .
i used to have psb tower speakers that played solid down to 40hz and a good NAD amp rated at 150 watts / channel. a powerful amp controls the speaker motion extremely well and has the power to create dynamic bursts even at low volume. the bass was spontaneous, tight and incredible and you could feel the impact from the excursions at really low volume.
the sign of a quality amp is to see if its rating goes up with a lower ohm spec, example 150 watts at 8 ohms, 200 watts at 4 ohms.  a good sign that the amp has a solid design and large enough transformers to have reserve power.