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

mtloriginal
DSP is a digital nanny not necessary for great sound, and it’s also generally a box of circuits your precious little signal runs through to allow the imposing of its designer’s opinion on all of your gear. My ego won’t allow it as I’m a pro concert sound engineer (also worth noting, a close friend has a well regarded DSP system in his rig and since he’s NOT a live sound engineer and in fact utterly hopeless about such things, I get it…although I think his rig sounds better with the DSD off). Although the lengthy articles preceding me may have covered this, it’s not that hard to get great sound with a sub, and the REL subs I use (apparently also the Vandy’s mentioned previously) get their tone from the amp driving the main speakers which is a good idea, but might not be all that important under 40 hz or so. I like the idea anyway. Distortion is minimal or, better stated, unnoticeable, and all you have to do is move the sub around until it sounds right to YOU. I use 2 RELs and I think that does help with standing waves (the sloping and very tall ceiling in my room also helps) , and I adjust the REL’s levels from time to time to deal with bass heavy or bass light recordings. My main speakers are efficient designs driven by an SEP amp and do 40hz before dropping off, and that’s right where I run the subs.
Guys, if you hate crossovers, get a sealed 2-way,plus a sub and don’t use a crossover at all.  Run the satellites full range, and only use a crossover and EQ on the sub.

You won’t get big gains in the amp's dynamic range, but you will avoid the electronics being in the way.

Best,

E
My new-ish current speakers (Sonist Recital 3s) use a simple first order "cap and coil" system with "real good" Snake River internal wire. They're efficient, dynamic, and need dusting from time to time.
My personal advice, considering your budget   get 2 martin Logan dynamo 300, open them and put inside a small cushy pillow back in the ointernal wall to dump internal resonances which will improve the tightness of the sub and put some cotton clothes on the firing port  so you seal them. The port for me only gives boomy and uncomfortable, not musical bass, maybe good for ht.
Then get the bheringher 2496 digital equalizer to adjust the frequency response according to your room , to do this you will need to download the audio tool to your cellphone, learn to use it, is not so difficult. Then spend a long time tunnig your subs with the recommendations given to you on the other comments.
Later, someday  get a preamp with phase tuning option, it is VERY helpful, I would say mandatory.
I own the ml sub with a pair of tiny paradigm Sig s1 v3 (is a sealed bookshelf) and could not express how good it sound.
Good luck!

I think there great for your movies.But that's just me. It did rock my room .