How many is much more important than which ones or how expensive. In other words, regardless of your budget its better to spend it on 4 than 1. Put another way you cannot find one sub that will be as good as 4 that cost 1/4 as much each. Search Swarm or distributed bass array.
System matching with 4 is a non-issue.
I'd suggest placing a phone call to REL and asking their opinion. REL customer service is very good.
Why not use the Avantgarde subwoofer? It's specifically designed to work with their horn loudspeakers.
Chilli, Any subwoofer that can match the volume you like to listen at will be fine. Most of us rarely listen over 95 dB and any pair of 12" subwoofers will do that easily. They all have adjustable gain. You just adjust it to match the output of your main speakers. It will require more power to reach the same volume but all the decent subwoofers are equipped to handle that. The 4 10" drivers you get with the swarm system will also do just fine.
So, unless you listen at 115 dB any decent subwoofer can be made to match your system. You are right to start minimally with two.
Aside from matching the listening volumes, in my experience the bigger issue is matching the ‘speed’ of the subwoofer driver(s) with your horn system. The suggestion of using multiple small driver subwoofers is much better than using one or two large driver units.
What deficiencies are you trying to address?You don't say whether the subs are meant to compliment the AG subs or replace them. If it is the latter, bear in mind this bit of info, as per Jim Smith years ago, that the AG Duo subs, (the sub 225 in my case), have "meaningful" output up to 500 hz. You could end up with a hollow midrange if your intent is to simply jettison the factory subs. I have no idea what "...negating a pair of subwoofers..." means.
I would do a little more investigating and proceed (or not) with caution.
I have 99db efficient horn speakers and use 2 RELs (bought used in mint shape for around 200 bucks each...a 10" and an 8") with 'em, and have never sensed a lack of "speed." They have input level controls along with phase and frequency adjustment...works swimmingly.
The quoted words of caution are from REL customer service. My I am suspicious but they recommended two of the biggest most expensive subwoofers they sell. The REL recommendation was seconded by a couple of friends. I am also considering SVS subwoofer. They did not seem to think that their subwoofer would have a problem keeping up with the AG Duo’s.
The reason I am not keen to buy AG subs is that I don’t want to have flexibility issues later if I migrate to a different main speakers.
Have you considered trying a pair of the HSU subs, they are reasonably priced and sound good with horn speakers.
I will look into HSU.
Acresverde, the goal is to complement the current speakers. Not considering replacing the bass drivers that coming with the AG duo’s
Kalali, the idea that a smaller subwoofer is faster is incorrect. Given appropriately designed motors a 15" sub is just as fast as a 10" sub. The 15" driver does not have to move as far to produce the same output so typically larger drivers have lower distortion not more. When a driver can not react to the signal in time what happens is the driver's response falls off or they start "breaking up." Most large drivers can go way higher than they are required to do. My 12" drivers will make it up to 700 hz before breakup and I only run them up to 125 Hz. Now you can get away using smaller drivers by using them in multiples. This only makes sense when you have to get the speakers within a certain form factor. Can't put a 12" driver in a tower speaker 10" wide. Otherwise, when it comes to low bass large drivers rule. For most residential sized rooms say 16 X 25 four 12" drivers will do the job by which I mean 105 to 110 db comfortably.
My experience with matching subs to just about any speaker is to go with an array of multiple subs rather than just a pair, as others have correctly observed. The idea is to have a large wave launch that can match the volume level of the much faster, smaller drivers without having to push them hard. If you have you ever heard the Infinity IRSs they are a good case in point, as the ribbons in that array are extremely fast.
I have AG Trios and they came with a two pair of dual 10" inch powered subs. That combination was just barely OK, and tended to fall apart at higher volumes especially with rock music. I suspect that is why AG came up with the idea of horn subs, but those beasts are huge and expensive. I solved the sub problem by adding another pair of dual subs, now 12 total and it was trans-formative, not perfect but much improved.
You might want to consider just picking up two pair of used 225s. They are relatively inexpensive on the used market. Also, I agree with Mijostyn's comment regarding speed and subwoofer size.
REL customer service recently told me they won't repair either of my subs should they ever need it. Hmmm...also, "speed" is a silly term and I don't think it's applicable to subs or really anything else in audio. I think some bass overhang in reverberant environs might be what makes people think there's a velocity issue, and many think it comes from cone material...it doesn't.
I am in the same camp as those that say quantity of subs is more critical than quality.
I have four subs in my system made by three different manufacturers.
"...also, "speed" is a silly term and I don't think it's applicable to subs or really anything else in audio."
Perhaps in your opinion and in your experience, but not in mine. I have tried various different combinations of three powered subwoofers; 12" and 15" - one 12" I own in a different system and the other two borrowed from friends, with my Omega Super Alnico Monitors, and in all cases I felt the subwoofers could not "keep up" with the single drivers and there was an obvious tonal lag in the portion of the bass delivered by the subs. I and the man who designed/built the Omegas express this phenomenon as "speed", others might call it something else. His recommendation was to use subwoofers either with two 8" drivers in a sealed box or multiple 8" (or at most 10") driver sealed subwoofers. Call it whatever you want.
The sub 225 appears to be a proprietary design that includes a 300Hz crossover. https://manualzz.com/doc/28390566/duo-fact-sheet---avantgarde-acoustic
I would think your goal would be the capability of a subwoofer that has output and control well above 300Hz and not simply high output.
Acresverde's experience and advise seems to be the only pertinent information to your goal since this is not just any speaker system.
Suggestion from first hand experience will save you from disappointment.
Beware and good luck with your search.
Blending a single sub with the mains and getting the tone/impact you are looking for is much more difficult in a small room. What is your room size? Are you planning to use REW for measurements and or some form of DSP measurement and equalization?