Subwoofers - Front Firing or Down Firing - Which Sounds Best?

Nix the down firing. That produces the most floor interaction which muddies the bass and obscures the midrange most especially with the suspended plywood floors found in most modern construction homes.

I built downward firing 4’ high cement cylinders with 8” drivers mounted in the bottom, raised four inches of the cement floor. Awesome sound, like cannons going off. Tighter than a bull’s you know what. 🐂 The back wave reinforces the motion of the sub.

Tip for the day: never move into a place with suspended wooden floor where your hi fi is going to be. Think ahead. 

+1 You can't have a good turntable rig on suspended floors. You can bolster it and reinforce it but there's no beating 5" of concrete. I tried once. Now I'm in the basement.
Not sure I agree with using any old subs, @millercarbon. I replaced an older REL sub with the new S3 and it is in a different league. Faster, taut, deeper, and more musical. 

I'm trying out a single Syzygy 10" subwoofer, with a stereo system on a concrete slab and engineered red oak flooring. The room is not exactly rectangular, but it's basically 18' W X 28' L X 9' H.
1)The single sub sounds best when it is adjacent to or between my stereo speakers, but the exact location does not make a lasting difference. (I can move the sub and think the new position is better, but the next day I can move it back with the same effect--I can't find a single best location.
2) There is a difference in the sound between forward firing and down firing, but it is more about the music than a single best presentation. For rock, forward-firing in-your-face bass delivers, but that doesn't mean it's better overall.
3) It is a fairly advanced sub which reads and graphs the room and is controlled by a smart-phone (which means one can listen anywhere in the room). The sub itself may be optimizable for the room, but it does not blend well with the stereo speakers. I can get drama--not a problem for Star Wars--but it's annoying for serious listening.
4) The experience has helped me understand why multiple subs would do better than one, and how the placement of multiple subs would be easier than one.
5) At the same time the experience has helped me understand how better quality--"faster, taut, deeper, and more musical" could help, and probably more than equalization.

Nix the down firing. That produces the most floor interaction which muddies the bass and obscures the midrange most especially with the suspended plywood floors found in most modern construction homes.

Interesting. Except mine fire right into the walls, as do Tim’s, as do all of Duke’s, and there is another very similar DBA design that fires down into the floor. The one thing they all have in common is exceptionally clean, clear, articulate and fast bass. The opposite of muddy. Oh well. Think and is don’t always agree.

You can’t have a good turntable rig on suspended floors. You can bolster it and reinforce it but there’s no beating 5" of concrete.

Okay. If you say so. But who says it has to be in the floor? And why only 5"?
https://systems.audiogon.com/systems/8367