Using Two Subwoofers with Two 2-Channel Amplifiers.

I am considering using two Subwoofers with two 2-channel Amplifiers using the speaker level inputs and outputs on the Subwoofers.  Each Amplifier is currently connected to identical pairs of Speakers.  Is it better to connect so that there is a dedicated Subwoofer for each channel (Left channels of both Amplifiers wired "through" one Subwoofer, and both right channels through the other), or dedicate each Subwoofer to an Amplifier so that L/R channels of each Amplifier go to a Subwoofer?

This is for a vintage system that I am using for music only.  I'd be happy to supply equipment details if that matters.  Thanks!
Sorry, but just to be clear, when to say "Mono" or "Monaural" you are referring to connecting Left & Right channels to each Sub correct? My initial thought was that this might confuse the Sub, but it sounds like you guys are saying that this is not necessarily the case (".. canceling standing waves..")
Depends on the connectivity options your subwoofers offer. My only high/amplifier level experience was with a REL Studio III using its proprietary cable. Maybe someone else here can answer your question.

By "standing waves" if you're referring those unusually bass heavy locations in your room they can be addressed by experimenting with subwoofer locations and feeding the subs a summed, mono, or monaural signal.

Eventually your setup will be as unique as your room and the system being used.  
Here is my setup which too me a while to get the sound up to the level that I was looking for......
2 Channel Stereo with 2 Channel Subwoofer Setup
Martin Logan Montis ESL Speakers which each have a 10" Driver with DSP and a 200 watt amp. (not enough low end, needs more)

2 REL S3 Subs
with one on the Left Channel, and the other on the right channel.

Using the RELs coming right off my Krell KSA-200S Amplifier's speaker connections. This is what REL recommends.

The RELs are placed on the inside of the Martin Logan Montis. Right next to each Montis. This allows for fill into the middle of the presentation.
Most say put the RELs on the outside. Bull, wrong. Tested and tried. The Stereo Subs should be on the inside and setup in stereo. REL has a video on how to connect the speaker outputs of the amp properly.

When I went from a Mono 2 Subs to Stereo 2 Subs setup..... WOW!! The difference is instant, and allows for a much better image. I cannot over stress how much better any speaker system can get with what they call "The REL Effect" using the input from the speaker leads from an amplifier. Paul the owner of PS Audio has a YouTube video about Subwoofer setup from the amplifer speaker leads. Oh, he glows when he mentions the REL Subs. The whole system blends and gives even the midrange a tangible improvement. The secret is adjusting the RELs to just be able to hear them, and then just back off on the REL volume control just a hair.
I know like I sound like a REL fanboy. I am. But they blend so much better than others. The are lightning fast, that's the secret. It's in the crossovers and the actual driver design. They can keep up with the Martin Logans fast transient response. The blend is what sends these out front in sub design for 2 channel audio systems.

JL Audio has a great sub, but for 2 channel music, JLs are an earthquake, and RELs are a part of your speakers, and they don't let themselves overpower the speakers. Take for example.... Revel Ultima Salon 2s. Great, but mind blowing with REL S series or Reference series in stereo pairs. REL has a T Series, and it works quite well at a much lower price point. But I wouldn't use them with speakers costing a lot of money. The S Series is a huge improvement. But, in the same token, you can get 2 Subs at a reasonable price. And 2 T Series RELs are better than no RELs are just one sub.

If you are listening to 2 channel audio (In my 40 years experience), 2 subs are required to get the proper soundstage and low end of the original recordings. Subs with 2 Channel Music should not stand out and act like a bully. Most subs are bullies, and that's why many audiophiles don't recommend having them.

Speakers that cost ten times as much as us mortals can afford have added 2 RELs to their system and come away with their jaw dropped. 

I would have not believed it myself until I bought them.

I now have 2 more REL S3 subs (total 4) that I have yet to take out of the boxes yet to experiment with.

The word from REL is that you can use multiple RELs and surround the room with their effect of giving body to the music. Maybe a few months from now..... I will place the other 2 RELs behind me, and see what happens. If you look hard enough, REL sells sometimes to dealers a recertified unit. Or watch the used audio websites for deals. Lastly, if you own Martin Logans.... it is your duty to pair them with a couple of RELs. I know of quite a lot of Martin Logan owners that are happy with what a transformation they experience with money spent. There are cheaper subs. Not a single one can put such a shot of Viagra into your speakers like these babies. Dennis
I've come to the conclusion that the fact I'm using two Amplifiers is irrelevant since the Amplifier does not "see" the Subwoofer(s).

It appears there are proponents for connecting two Subwoofers both in stereo and mono, so I will most likely experiment myself.

I initially asked the question because I was thinking in terms of a vintage system I have, which has no Sub outs on the Pre Amp, and only room for one set of speaker connects on the Power Amps.  Thererfore, I'm looking for Subs that have Speaker level Inputs and outputs.

A side note: Its been frustrating researching Subs for this music only system.  Everyone always talks in terms of "This Sub will bury that Sub".  I don't want a Sub that will bury anything.  I just want them to supplement a vintage Two Amp, four Speaker music system that lacks low end.

There seems to be allot of love for REL.  I had decided on SVS to supplement a different music system I have that features Marin Logan Motion 60s.  I will have to look into the REL's.  Thanks.
SVS is a great choice.  They make a great sub.  I had two REL subs and could never get them to integrate properly in my room no matter where I placed them.  I now have two JL Audio F113 v2's and with their DARO technology, it was a breeze.  Now most people don't even know they're on, the integration is so seamless. 
Audiostick 7-21-2018

Is it better to connect so that there is a dedicated Subwoofer for each channel (Left channels of both Amplifiers wired "through" one Subwoofer, and both right channels through the other), or dedicate each Subwoofer to an Amplifier so that L/R channels of each Amplifier go to a Subwoofer?

Audiostick 7-27-2018

I’ve come to the conclusion that the fact I’m using two Amplifiers is irrelevant since the Amplifier does not "see" the Subwoofer(s).

The amplifiers won’t see the subs in the sense that the subs will present the signals provided by the amps with a very high impedance, and consequently draw a negligible amount of current from them. However, if two amplifiers are connected to the same sub I can envision several kinds of ground-loop and other ground-related issues that may arise, depending on the designs of the particular amps. Keep in mind that with that approach the negative output terminals of the two amps would most likely be connected to each other, via the sub, since both of those terminals would presumably be connected to the sub’s internal ground. That doesn’t seem like a good idea to me.

And if by any chance the amps have balanced or bridged outputs, meaning that their negative as well as their positive output terminals have full amplitude signals on them, blown fuses, damage, and/or pyrotechnics would be entirely possible with that approach.

-- Al