Warning, small rant ahead.
The first I'll talk about is if the actual Team Rocket is weak compared to Ash, to signify his gain in power over the years. Because he managed to foil their plans. (Even if it was just dumb luck most of the time, hell, the 'incompitent' trio are actually pretty decent members, and most of their plans would work if they didn't follow Ash and Pikachu, but I'm getting off topic here.) But later on, he can actually take them down and get them captured.
Or it could go the way that I think it might go. I think I heard somewhere that Giovanni was the most powerful trainer in the world. Don't quote me on that, but if this is true (Which it might be, because he never fought seriously in the anime.) than he'll have hell to go through to beat the members, if they were also powerful, since the trio that follow them are likely at a low rank. Viscious (villain of Pokemon 4ever) is a Rocket Administrator, and he was tough to beat, granted that was in Johto, but they too could have improved over the years.
Okay, since it actually took Ash a year to get through Kanto, (Somewhere in the dub, before fighting the 'Incompitent' trio for the eighth badge) I assume it took a year to get through each major region. I know there's a flaw in this, but this is what I go by. Both the Orange Islands and the Battle Frontier, being fairly small would probably be somewhere between 3 and 8 months. I wouldn't ever say a year, but I go highest case for OI, and lowest for the Kanto BF.
The Battle Zone, if they go there, would probably take around the same time as the Kanto BF, maybe a little longer, so I'll say 4 months. Now remove every season before Hoenn from the equation.
Hoenn and Sinnoh gives them two years and the combined BZ and Kanto BF would be seven months. Now assuming that they go after Team Rocket immedately, than Giovanni and his admins have had a range of two years and seven months to three years and four months to get stronger. I know in this there can be flaws, but this is just my opinion on the matter. This theory can easily be disproved. Now, If Ash got to where he was in Johto, to where he is now in Sinnoh skill wise, think of what criminal masterminds could do, if they took time to train or learn. They'd be monsters! Now, the fifth Generation, I'm pretty sure will be coming out, so let's factor that in as well.
Another year, plus a possible six month side story for HG/SS, and another 3-8 month side story. That would be within the range of 1 year, nine months, and 2 years, 2 months. Add that to the equation above and they have a range of 4 years, four months and 5 years, six months. But that's just estimation. There is also a chance for another season, but if this keeps up, I will be getting off topic.
Point is, they have had a lot of time to get stronger than ever before. I don't think Ritchie could fight against TR like Ash did, because Ash is the main character and will likely beat down TR, and Misty fighting to surpress TR is laughable, because she, while she is a good trainer, would lose to Ash in a heartbeat at this point. Sure, she beat Ash in the Whirl Islands, but he could have gotten a lot better in comparison. Sure there is a cast of minor characters to try and surpress TR, but they can't really do much, with the exception of the Elites and the Frontier Brains.
Now, add this to TR. If each team of grunts were as good as Butch and Cassidy, or even the incompitent trio, they could actually be a threat. Like I said earlier, their plans would have worked if Ash wasn't there, just imagine thousands of that, and you have Team Rocket, added with the fact that there are much better agents in Team Rocket anyway.
Let's go back to Giovanni. Even if he isn't the most powerful trainer in the world, he is still a powerful man. He has powerful pokemon and a lot of resources, and if they really want to make him a threat, than he also might have people in the government. Add to the fact that he never fought seriously, or with his own pokemon. The pokemon he used against Gary are probably used so that people have a chance. He is a gym leader after all, and he is likely to be at a certain level, so he doesn't use his best team. He never used Persian either, which means that it is either really powerful, like Wigglytuff in PMD2, or for show. Either way, he is powerful, and commands thousands of people! Ash is a berserker, he'd try to plow through them all before fighting Giovanni! With the help from any Elite 4, he could probably do this, but the only person who would probably help, other than his friends, is Lance, and a few Frontier Brains. they is powerful, that is true, but to fight off possibly hundreds of people, a few people possibly at the same level, and someone stronger than them, all without rest? Unless you have the luck of the gods, that isn't possibly going to happen!
Not to mention their judgement. Rockets are supposed to be ruthless, which gives them a huge edge over the heroes and supporting cast! They will keep on attacking unless they are put down! Weakening the heroes pokemon even further! There is Paul that could fight them evenly, seeing as he fights somewhat like them, but even he has his limits. If they were powerful two to five years ago, they'd be much more so this time around!
Now, there are things in here that can be countered, but this is just how I think it would go down.
