RBY
Starmie was once seen as a Special Sweeper par excellence, but thanks to Chansey's absurd populatiry, Starmie is now better seen as a defensive "glue" Pokemon that keeps itself going with Recover rather than as some frightening sweeper. It makes a good sleep-absorbing lead, as it scares Gengar with a faster Psychic, outspeeds Jynx and resists its attacks, and scares Eggy with Blizzard while taking little damage from Psychic in return (Mega Drain variants can be annoying, though). It also outpaces and paralyzes Tauros while taking its hits better than the other Recoverers (it isn't guaranteed to be 2HKO'd by a Bslam-Hbeam sequence), it can duke it out with Alakazam in a stall war, it's an okay answer to Golem/Rhydon once Eggy is gone, and it's also probably the best answer to Slowbro RBY has to offer. However, you'll notice that Starmie has major 4 moveslot syndrome here. It needs a STAB to do meaningful damage to Snorlax and Tauros, with Psychic being the choice if you also want to hit Gengar, and Surf the choice if you also want to hurt Alakazam. It also needs Thunderbolt for Slowbro and other waters, Blizzard for Eggy, Thunder Wave to get the most out of its support role, and Recover to stay alive. There's also the niche Reflect and Light Screen for walling certain things, but you don't even have room for all the standard attacks you could want, so how could you possibly fit those on your set? In short, Starmie wants to Special sweep, but Chansey exists, so it has to settle for abusing its movepool as a "quick fix" against myriad offensive threats, but its 4-moveslot syndrome forces it to pick and choose which threats to check.
GSC:
Whatever attacking prowess Starmie had in RBY is totally shafted under King Snorlax's reign, not to mention that Electrics get a buff and things such as Umbreon and Blissey exist to wall it perpetually. Furthermore, on defense, there's much bulkier Water-types, such as Suicune, that are
much better suited to taking on heavy-hitting Physical ground-type threats. So what keeps Starmie OU in GSC? Simple. Rapid Spin. Starmie is one of three Pokemon to effectively play the GSC Spikes game, the other two being Forretress and Cloyster. Unlike the other two, who get Spikes in addition to Rapid Spin, Starmie only gets Rapid Spin, but is much longer-lasting thanks to Recover in addition to providing better defensive synergy. Its Psychic typing and blazing Speed let it step in against some obscure threats such as Machamp and Charizard that the other two wouldn't really be able to handle, and its STAB Surf still allows it to function defensively as a Ground-type scare. It also gets to support its team with its fourth moveslot, with Thunder Wave and Reflect being some of its more prominent moves. Overall, Starmie is kind of mediocre, but with Rapid Spin and Recover, it carves its niche as the best Rapid Spinner in GSC, even if it does struggle to spin against Forretress.
RSE
Still a premier Rapid Spinner, but it's also bolstered on offense, too, thanks to the EV system robbing many Pokemon of Special Tankiness. Snorlax is still pretty popular, though, and Blissey is also mega-popular, plus Regice exists, so it's rarely getting a chance to Special sweep, but there's still teams out there that rely on Celebi and Zapdos to take Special hits, so it
could be threatening. It's still better off focusing on its role as a reliable, Recovering spinner, especially with multiple layers of Spikes being introduced, but ADV also brought with it the extra-bulky Dusclops, which Starmie is kinda powerless against. Clops isn't so popular in ADV at the moment, but he's historically a pretty big deal, and he makes Starmie's role as spinner pretty difficult without Pursuit support. I guess it's also worth mentioning that it outpaces Gengar and +1 Adamant DDTar, putting it into a potentially game-saving Speed tier.
DPP
DPP was a blessing and a curse for Starmie. On the blessing side, access to Life Orb allows it massive damage output from its otherwise decent-but-not-great Special Attack, and a metagame obsessed with Speed and hard-hitters makes its Speed much more of an asset while leaving its primary checks, Blissey and Snorlax, less popular than they were in prior generations (though they're still pretty prominent). Even then, it gets access to Trick and Choice items to screw over those defensive mons, and is a very good revenger with Scarf and attacker with Specs before using Trick. On the curse side, though, while Starmie still gets Rapid Spin and is indeed still one of the best spinners in the game, it's got even better spin blockers in Rotom-A and Spiritomb to contend with, plus the ever-present ScarfTar and, to and extent, Scizor can wreck it with powerful Pursuits. It's less the reliable spinner with Recover this generation and is instead better known as the spinner that can wreck spin blockers with STAB Hydro Pumps, but it's hardly unique in being a spinner that's able to beat spin blockers. Overall, Starmie is less effective in its traditional support/Rapid Spin role, but it gets new toys and a faster-paced metagame to make it the legitimate Special threat it always wanted to be.