First of all, according to this page of PS! OU Usage for February 2017,
| 88 | Gastrodon | 1.59471% | 34007 | 1.595% | 25991 | 1.642% |
| 131 | Quagsire | 0.95231% | 20308 | 0.952% | 15047 | 0.950% |
so, Gastrodon is used more in OU than Quagsire.
Further, Smogon lists Gastrodon in NU, whereas Quagsire is stuck in PU. PU ranks lower, so once again, I fail to see how your claim that more people use Quagsire over Gastrodon is legit. Of course, I'm not denying that you probably encountered more of the Sausage Tailed Sire than the Slug, but statistically, it is not so. Further, both Pokemon have taken a hit this generation in usage due to the ultra-powerful new entrances, be it the Mega Pokemon or the Ultra Beasts. From what I'e noticed, defensive and stall teams are on the decline, meaning they are just not bulky enough to take a LO Lele's Terrain boosted Psychic, or withstand the all too powerful Z moves that can quickly crumble defensive Pokemon.
That said, this is strictly in the upper tiers. As for the lower tiers where most of the older Pokemon stand, things might be a little different. Now, JarJar is perfectly correct when he said that Unaware is invaluable. Compared to Storm Drain, in more defensive teams, Unaware stands out as the better ability, wasting all of the opponent's stat boosts.
Further, since both of them carry Recover, it is not easy to choose one over the other. Also, their spreads are different, but very slightly so. As you yourself pointed out, Quagsire is Physical based, whereas Gastrodon is more of the Special variant. Most boosting moves are physical (SD or DD or even Bulk Up or Curse) meaning you see Quiver Dance less, so a defensive Unaware makes perfect sense rahter than a Specially Defensive non-Unaware variant.
tl;dr : There are some reasons why Quag > 'Don but to be honest, the Don is used more anyway.
EDIT: As sumwun pointed out, statistics differ when comparing plays ranking higher than 1800s.
In that scenario:
63 | Quagsire | 1.83606% | 20308 | 0.952% | 15047 | 0.950%
118 | Gastrodon | 0.35285% | 34007 | 1.595% | 25991 | 1.642%
So you're right about its added usage. The reasons for that, remain as mentioned already before edit.
Further, proper tiers are yet to be defined for all Pokemon, which might take some more time to get sorted, mainly because most of these are not available in the main Gen 7 Games. Thus, Gastrodon and Quagsire are classified as "New" (Unlisted) Pokemon, as seen in the PS! Teambuilder.