Which subwoofer should I get?

REL; set it up properly and forget about it.  Doesn't draw attention to itself, enhances the overall system, and no "app" needed.

The biggest flaw of almost all subs is the lack of a high pass filter for the main speakers. It's hard to do when you don't know the main speakers. But properly done a high pass will make the subs/mains twice as good because the main woofers have to do orders of magnitude less movement resulting in instantly recognizable better sound in the new bottom octaves of the mains. So I'd go for a sub with a high pass or find a way too add one your self.

Also, this is sort of taste. Closed box woofers are more accurate than ported ones(or passive radiators). But they don't sound as rich. Closed box subs are rare. Rhythmic makes them. There must be a few others.

I'm definitely getting some mixed messages about the utility of getting a sub that is app controlled versus the RELs without app control. That's ok, just want to acknowledge that there are differences of opinion (what else is new with audio?) 

If I go with REL, simply based on specs, it looks like a pair of S/510's which are rated at -6db @ 20HZ are obtainable on the used market for $4k for a pair. This is significantly less than the Carbon Specials and would allow me to purchase a pair immediately rather than waiting. As another data point, the S/812 would be around $4.5 - 5k for a pair.

If I decide to go for the RELs, what would you advise is the best model for my room and music listening preferences, factoring in the cost differences?

Thanks again to everybody!!

I realized I have a separate but related question. My integrated has two subwoofer out RCA connectors. The manual states only the following about them: "This output allow you to connect an active subwoofer or a second power amplifier." 

Does anybody know if these are "high" or "low" level outputs?

Given that the T/5x's are only rated -6dB at 32 Hz, I wonder if this is enough low end given my speakers and room? On the other hand, I'm a little concerned that a pair of Carbon Specials may be overkill for my situation (and a lot more expensive). Thoughts about this given my room size and need for music only?

Some thoughts — a sub that’s down 6dB at 19Hz at the price of the REL Carbon Special is nothing “special” at all when many other very good subs at less than half the price go down to an honest 20Hz and below.  A lot of spatial cues that get unearthed down there will be lost by many REL “subs.”   Many don’t realize that while not many instruments play down into the 20Hz region, there is still important recorded musical information that resides down there that plays a big part in improving imaging and an expanded 3D soundstage.  I wouldn’t worry about overkill for your room — just buy good subs that can get you to an honest 20Hz (-3dB) and if properly dialed in not only will they not overpower your room, they will work much less hard and with less distortion than smaller subs.  As for SVS subs being too sluggish for a 2-channel system — horse hockey!  I and many others here have gotten excellent results with SVS subs when properly dialed in, and all reviews back this up.  But you already got pleasing results even with a ported PB2000 so you probably already know this.  Just my experience and $0.02 FWIW.