Meowth only really laid serious damage once - an episode in DP where he used the move "Fury swipes of love" to take out Ash's Infernape and Staraptor. And that was because he was infatuated by a Glameow. Other than that he rarely battles and on most of the occasions he does he ends up loosing easily e.g. against Tyson's Meowth. Since part of the skill of battling is to be able to interrupt or outmanoeuvre an opponent I'd argue the ability of Ash and friends to consistently do that demonstrates a major strength difference between them.
He also defeated a Persian, decimated a large amount of Team Plasma's squad and fainted Barry's Empoleon (a steel type), all with just a single Fury Swipes. Even some he loses aren't complete curb stomps all the time (the one time he hit Pikachu with an attack it blatantly done a lot of damage, and he even tanked Fennekin's attacks by just Fury Swiping them to bits once). Meowth can be powerful in battle, but only when he gets his head in gear and focuses on how to use it, which is rare.
Tyson's Meowth seems a rather unfair example since the whole premise of that one was that he was stronger, suaver and just all around better than Team Rocket's Meowth.
Certainly Team Rocket are not being portrayed as being as incompetent as they were in generations prior to 5, so it's not unrealistic Inkay beat Mantric. The point I raised was that Inkay has nothing on Pikachu even if it can beat other Pokémon. Inkay may have a couple of times gained a slight upper hand when battling against either Pikachu or one of Ash's other Pokémon, often due to Team Rocket using underhanded tactics but in all situations their plans and strategy usually fail mainly due to the fact that Ash's Pokémon are stronger.
Like you said though, manoeuvres also play into it for Ash's Pokemon. And you also forget the number of times Ash's team broke the rules in order to stop Team Rocket, using more than the same amount of Pokemon or personally intervening themselves (not that I'd complain about them 'cheating', they look stupider when they try to play by the rules against villains trying to attack them). Even at that there's plenty of times the Trio still had them on the ropes until plot armour saved them with an evolution or the POTD intervening.
I could make the argument that not only could neither side 'cheat' in this situation, but James was playing with someone with a more effective team strategy than what Jessie usually offers which made the difference and nerfed the heroes' ability to just dodge and out agile them. With that it became a case of raw power, which Inkay could better match.
I could make the same argument for say Wobbuffet, who is constantly blasted off by Pikachu, but anytime he's ordered to battle properly against him, he can tank nearly everything Pikachu throws at him.
Tackle is still a relatively weak move even if it's been used decisively in the anime before. If it were psybeam the amount of damage taken might have been more understandable but one tackle on Pikachu brining the battle to the point of it being hopeless for Ash and Serena but for Eevee evolving. That's a big stretch to the point of being plot amour to get Eevee to evolve dramatically.
Except Psybeam was the move used when they were trapped in Cotton Spore. When Inkay used Tackle, the damage was already done.
Yes plot armour is involved sadly, it's involved in the anime all the time. Even straight afterwards it's involved by Sylveon instantly healing all it's injuries and being completely unstoppable upon evolution (my best guess is, like Noivern, it won't be nearly as strong in it's next battle). But hey, plot armour FOR Team Rocket instead of against them is at least a change.