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

Sound travels at 1125 feet/second per Wikipedia. That means wavelength is 56 feet at 20 hz and 14 feet at 80 hz. Resonances are caused by reflected waves reinforcing the direct wave. If your room has, say, a 37.5 foot dimension, expect to have a peak at 30 hz, 60hz, and possibly higher multiples of the resonant frequency.

When I was in my twenties I bought a real time analyzer and measurement mic so I could test the calculations. In that period I upgraded from B&W N804s to B&W N802s. That was a change from a front port to a down port. Since the port output is at subwoofer frequencies I consider this a reasonable comparison. The 804s had atrocious in-room measurements. They were actually flat at 20hz. All over the place from 20-100hz. 30db swings in my room. The 802s measured far, far better in the deep bass. They were actually very close to the published spec. They hit the -3db point at almost exactly the published point and the overall deep bass measurements were far smoother. The only plausible explanation is that the down-firing port doesn’t excite resonances to nearly the same degree as a front-firing one. Which means direction matters, even at very low frequencies.

freq/length in feet
20 56.25
30 37.5
40 28.125
50 22.5
60 18.75
70 16.07142857
80 14.0625

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.