I've used both, and while Cyndaquil/Typhlosion were definitely good, Feraligatr was on a whole different level. First off, Feraligatr's coverage options are waaaay better than Typhlosions. Surf, Waterfall, Crunch and Ice Fang will decimate almost anything, and hit a lot more common opponents than Aerial Ace, Dig and Shadow Claw (Typhlosion's options). There's also the matter of weaknesses. Plenty of Pokémon in HGSS carry Rock and Ground attacks, but few carry Grass and Electric, meaning that it's easier to take risks with Feraligatr in battle than Typhlosion. Not to mention that Feraligatr is waaaay tankier and more versatile. Typhlosion's Fire attacks may be wicked powerful, sure, but when put in a situation where "kill it with fire" isn't a good option, it has a major handicap. Feraligatr, however, has tools for lots of situations. Just with Surf/Waterfall, Ice Fang, and Bite/Crunch, it can beat Morty, Jasmine's Steelix, Pryce's Piloswine, Clair, Will, Koga, Bruno, Karen, and Lance. Cyndaquil/Typhlosion are strong at the beginning of the game, but their effectiveness tapers off as it goes on. Totodile/Feraligatr are weaker before they get their good moves, but once they do they can easily solo the Champion and most of the region, which Typhlosion cannot do, and I think that's enough to prove that Totodile the best starter in HGSS.
One more thing — there are no better Water Pokémon in HGSS. Gyarados and Lapras are the only things that come close, but Gyarados lacks Crunch and has a 4x Electric weakness, making it an unreliable counter to Dragonite. Lapras takes forever to level up, and grinding is already a pain in these games. Lapras is probably the only Water-type in HGSS that I'd put in the same tier as Feraligatr. Vaporeon, Slowbro, Slowking, Starmie, and Lanturn are all good Water-types, but none of them are better than Feraligatr.
I'm not trying to say that Typhlosion is a bad starter Pokémon, and I won't deny that when it comes time to roast marshmallows it does so extremely well. But Feraligatr is just absolutely off-the-wall crazy in HGSS.