Woofer on the side or bottom to augment 3way

Suppose you have a 3way (1 + 4in + 8in for example) design but want to augment the bass with an extra 10in or 12in sub woofer that will cross over at a fairly low freq. at about 80 - 100Hz.

Is there any inherent advantage for the subwoofer to be on the side or at the bottom of the cabinet?

Visually, with the sub woofer on the side, the cabinet could be made slimmer which improves the aesthetic.

But in term of acoustic, which would be better?
 
Geddes: “The mains should be designed for the best possible direct field with as flat a power response as possible. Equalization of the mains could only make them worse.”

You will get the best soundstage if your 3-way front speakers cover ~30Hz - 20kHz
Suggest: 1" dome + 6" sealed midbass + 12" sealed woofer(-F3 = 35Hz) ... use the wider baffle to improve the entire speaker.
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You will get "slightly" more uniform room(side walls, rear wall) effects if all drivers are on the front baffle.
Woofers benefit from floor gain: low placement = less than 1/4 the ceiling height.

If your main 8" woofer speakers already cover the 60Hz range, your room will produce smoother deep bass equalization if you can
move a stereo pair of separate box subwoofers around the room. Many 8" woofers produce < 40Hz bass in a ported cabinet.
 
A few pics of 12" side woofer designs with modest width front baffles. The 12" SB_Acoustics SB34NRX75-6 is designed to produce -F3-35Hz in a 3.5cuft SEALED cabinet. A few expert designers praise this driver ... sealed.
 

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Side mounted woofers allow for higher frequency distortion components to have a less direct path to the listener as they'll generally be more attenuated/diffuse than when on a front baffle. The low-pass characteristic imposed by side mounting has other advantages for crossover design, particularly passive where sub-freq devices are very hard to manage (huge $$ inductors). Ideally one on either side with good mechanical coupling adds additional reduction in excitation energy for the box.