I use these under my subs with great results:
I used a Sub Dude with my REL B3 but didn't note any improvement versus the sub on the carpet. The floor is concrete. Of course, I never could achieve the result I wanted with the B3 either. I now have a pair of Gallo subs which actually do what I want. They sound and look great on black marble tiles.
I'm afraid to look and see....
Actually my forward firing sealed M&K sub needs some repair work and has been taken out of active duty for now.
No doubt subs, especially one that fires downward in any shape or form, will interact strongly with the floor, especially elevated wood or plywood construction floors and placing same on various platforms that help to attenuate that interaction when needed helps if other available controls or level adjustments prove insufficient alone, which may well be the case.
Same sub say on ground level carpet covered concrete foundation may need nothing special underneath to help tame it.
So what specifically is under the sub in addition to the floor may not matter as much case by case as having the right thing under there in each unique case to help tame interactions with the floor if needed. I would expect the need in general to be less or nil in general on a concrete foundation/slab. There may well be other acoustic artifacts of teh room beyond just the floor though that come into play. SO you can apply some general rules, but hard to say for sure what is best with out hearing.
I have speakers with bottom ports that I place on more rigid tile platforms to help tame floor interactions when used on my second level with typical plywood/carpet floors, yet same speakers in my basement level on concrete foundation with thin carpet need nothing more underneath them, though I do apply other tweaks as needed there in order to get bass levels just right.
I have my front firing REL on the wood floor in a smallish corner (formed by a gas faux fireplace) behind a main speaker...simple pads on it so it doesn't scratch the wood, and it works for me so I've never even tried any other way. I do put my mains (Silverline Preludes) on butcher blocks with Vibrapods under the speaker base to lift 'em and decouple things...the "pods" turned out to be a very good thing for some reason.
Two different approaches in different systems. In the office system, I use a Sub Dude under a Velodyne. It made a very surprising and significant, instant improvement to tighten up the bass, correct for more tuneful bass, and reduce boom.
At home in the main system, I use ASC Sub Trap under a JL Audio F112. Also helped, significantly, reduce boom and tighten bass.
I am in this business for over 15 years of time. In the past I sold a lot Rel subwoofers. Beside this I have done many different tests with subwoofers as well. I would only choose for downfiring for surround. When you have an ols house or woodenfloor you get more drive. The floor makes the low freq even more pronounced. Even with music it can give some more fun. But..... when you want the best what i call steatlth integration with your speakers a closed subwoofer with only one bass unit in front is the way to go. Also in timing and speed this works a lot better. When you have a very fast subwoofer in respons you can use to higher freq. I use mine from 16 hz till 140 hz. From 80 hz low freq. become touchable. With audyssey pro and using it till 14o hz I have full stealth integration with my subwoofer. In the past I thought that this level never would be possible. Time and technique changes and sometimes dreams can come true.