It speed ties with Jynx (who just puts Shiftry to sleep) and Primeape (which doesn't care about sucker punch) and OHKOs both, and it has a 75% chance to OHKO offensive Xatu. It cleanly 2HKOs defensive Xatu, which can beat non-SD Shiftry. The faster variant just bops him with Signal Beam anyways. Being faster than Rotom in order to not get burned is huge, too. It does up to 85% to Kangaskhan WITHOUT a boost, which is a single stealth rock proc and some chip damage for a clean OHKO. Being able to reliably bring Vivillon down to sash is amazing, too, and something Shiftry cannot do. Lilligant, which it wants to switch into anyways, is a strange situation because it can win if it sets up QD on the switch and runs HP Ice, but if it does run the more common HP Rock or Ground, it can't touch Sawsbuck. Less so if it dares to click Sleep Powder as long as the buck is alive. Not having to fear Colbur Mesprit's Signal Beam is pretty nifty, too. I don't know if you count those mons as irrelevant, but I encounter them on the ladder on a daily basis. Also not trying to be a smartass here, but this seems pretty important to me.
The problem here is that Sawsbuck struggles to secure matchups with its superior Speed.
- Relying on speedties to best things like Jynx and Primeape are shaky enough, but this is worsened by those two happening to be effective wielders of Choice Scarf, whereas Sawsbuck is not (and of course, Shiftry has the advantage against Scarf Jynx). What's more, if you say that Shiftry has to worry about Jynx's Lovely Kiss, Jynx also has to be conscious of Early Bird allowing an immediate Sucker Punch, so Jynx can't always breath a sigh of relief just because it won the first 50/50.
- Offensive Xatus are not likely to be carrying Colbur Berry (they don't have the bulk to effectively make use of it anymore), so they are still at risk of Sucker Punch. Defensive Xatus aren't reliable checks either, because if they've lost their Colbur Berry, Sucker Punch stands high chances of OHKOing. If you wish to bring Thunder Wave Xatu into this argument, it would only hurt Sawsbuck's situation more.
- The Kangaskhan matchup is more in Sawsbuck's favor than Shiftry, but Sawsbuck is still not able to OHKO Kangaskhan, whereas Kangaskhan's Silk Scarf Double-Edge can KO Sawsbuck after LO recoil, so the Kanga user can just trade if they really want to. If Kanga is in range of a Jump Kick KO, Kanga can still do lasting damage with Fake Out + Sucker Punch before biting it. I am assuming you're talking about Jump Kick instead of Double-Edge here (judging from the 'upwards of 85%' you said Sawsbuck'd do), because Double-Edge makes it far more unlikely for Sawsbuck to make it out alive from this matchup.
I'm just going off my gut here, but from the sets Orphic described (SubSD, SD 3 attacks), I am presuming SubSD to be running Return and SD + 3 attacks to be running Double-Edge while also having Jump Kick, so I'm not sure if Double-Edge'd factor into this Kangaskhan matchup. Orphic mentioned an SD Lum set too, so you may not even guarantee that LO is present in the calcs.
- I mean yeah Sawsbuck can prevent Sash Vivillon from getting more than one Quiver, at the cost of its own life,
assuming the Vivillon user is keen on staying in. Meanwhile, I can argue that Shiftry can stop a (broken-)Sash Vivillon that has set up, so this argument can still go both ways.
- While no longer Lilligant's most popular Hidden Power, you cannot always discount HP Ice, as HP Ice can still target mons that Sleep Powder does not affect (mostly Grass-types and Xatu) and doesn't drop the Speed IV. Also HP Fire Lilligant is a possibility as well. While Sawsbuck may deter Lilligant from immediately spamming its STAB, it is absolutely helpless against +1 Lilli with a super effective Hidden Power. Shiftry can inflict major damage with Sucker Punch on any Lilligant variant (provided your predictions aren't off by a mile), and still not fare badly against the non-SE Hidden Power Lilligants as well.
- Yeah Sawsbuck is not in nearly as much risk against Colbur Signal Beam Mesprit, but it still has to watch out for things like Ice Beam, LO Signal Beam, Thunder Wave, and whatnot, so it's not so much a point for Sawsbuck than it is for Mesprit.
So the biggest thing differentiating them is Sucker Punch. And that's where the speed comes in again. Shiftry wants to sucker punch Rotom and Jynx, but can't because of Will-O and Lovely Kiss. Sawsbuck just bops them if he wins the speed tie. Same with Evire, though I can see how that is less relevant. I think it's also huge Sawsbuck has the ability to regain HP with Horn Leech, and my post further up shows a scenario against Weezing where that's important.
Why Shiftry would want to Sucker Punch a Rotom? It's not at risk of being immediately KOed by anything Rotom commonly carries. You'd pretty much want to use Knock Off on any Rotom unless you know it has the rare Signal Beam, which is found most often on Choice Rotom anyway, so it's not like they can play around the Sucker Punch.
One more thing I'd like to address: you mentioned
non-SD Shiftry. This implies that Shiftry has an effective immediate attacking set, unlike the case with Sawsbuck. I mean, look how weak this thing can be if unboosted in comparison to Leafeon, another Grass-type attacker reliant on boosting:
252 Atk Sawsbuck Horn Leech vs. 0 HP / 0 Def Eviolite Rhydon: 232-280 (66 - 79.7%)
252 Atk Leafeon Leaf Blade vs. 0 HP / 0 Def Eviolite Rhydon: 304-360 (86.6 - 102.5%) -- 12.5% chance to OHKO
Of course, this power issue is less glaring with Life Orb, but your suggestion of Life Orb Double-Edge means that using the move would take its toll on Sawsbuck very quickly. Despite Horn Leech's healing offsetting LO recoil, the fact that Orphic prefers Lum Berry is truly indicative of the importance of setting up over immediate attacking potential for Sawsbuck. I mean having a decent set-up sweeping moveset is fine, but having an effective immediate attacking moveset alongside it would be immensely helpful to decide a mon's viability (examples include Charizard, Samurott, Scyther, and of course, Combusken), and I believe Sawsbuck lacks the latter quality enough to be ranked too highly.
This ties in with your Cacturne nomination, because coincidentally enough, it possesses both powerful immediate attacking capability and dangerous setup sweeping potential. Like Sawsbuck, Cacturne manages to partially benefit from the drops as well: it can take advantage of Gastrodon to deter Scald, can beat up the slower Aggron, and can take on Smeargle (although its lesser Speed does put it at less of an advantage in comparison). While still largely overshadowed by Shiftry, I think Cacturne remains decent enough to remain in B-.