Well this all depends. Would be allowed to pull Pokemon from games I've played out to to battle with? Do I still have to own the games or save data? Will they remember and obey me? Can use any game or just certain ones(like the color games)? Will they be restricted to 4 moves or more multiple moves? How will they differ, if at all from the Pokemon from Special's world? Is it a sporty, game style, trainer-commands-Pokemon battle or a trainer-gets-involved, anything goes battle?
Or! Do I have to catch new Pokemon from the Pokespe world? If so, that'll open up whole new problems because I wouldn't stand a chance if I had to start from scratch. The problem is, they're all strategists, they come up with ideas.
So just because everybody else is doing it, let's say I have access to any Pokemon I've ever played with.
Red: Red's the battler. So unless God or Arceus or Hidenori Kusaka or whatever higher power if any is in charge me at the time decides I should win, it'll be a miracle, I'll have won by the skin of my teeth. But If we're going by story details, I would lose because he's the first and strongest main character. In terms of skill, Red's strategies still impress me and I'm not sure I would win, or even force him to think hard. So yes, I would battle Red, screw the outcome of the battle. Though there is a 99.9% chance I'll lose.
Green: Green's the Viridian City Gym Leader, Red can't refuse and Green doesn't really have a choice. Though chances are Green would battle me with his Gym Pokemon unless it was serious. In which case even if I beat that set I wouldn't have taken Green at his fullest. So yes I would battle Green but I don't think I would win against either of his teams, though I stand a better chance against his Gym team.
Blue: If I had pulled Pokemon from my old Blue version, and felt the need to go Blastoise vs Blastoise, I might challenge Blue. But forgeting that her Blastoise is air born and mine probably isn't, the key word being probably, I would be at somewhat of a disadvantage anyway, the real danger to look at, is her Ditto. Though to be honest, after being reunited with your long lost parents and having a lot of other interests, I wouldn't wanna bother her just for a battle. So no, I'd just let Blue go live her life. I might talk to her but her family is more important.
Yellow: Yellow is a pacifist, and her powers, even with a level 93 Gyarados or 100 Mewtwo I still run the risk of losing if(and only "if") she's serious about beating me, and it's an anything goes battle. Healing optional, level altering mandatory but she still has more going for her. But battling my favorite fictional character is the last thing I would wanna do, I'd much rather talk to her and get to know her.
Gold: Gold probably has some strategy desguised as an idiotic mistake ready, but I might win if I stay on my toes and use the right Pokemon. I have no idea what a battle between Gold and me would be like. And for that reason, I wouldn't battle Gold, I'm not so sure I'd even socialize. I mean, I like Gold but I don't know what kind of chemestry we'd have so... I don't know.
Silver: I wouldn't want to bother Silver either, he has more important things to do what with Giovanni being his father and all. If I did battle him though, and I if I did overcome any beserker way of battling he has, his story is like the other characters, the strategy that is incorperated into his battling. So no, I wouldn't challenge Silver, but for Gold and Silver, I'd just have to see how the battle goes.
Crystal: She's a really busy person, so I wouldn't want to bug her ethier(wow I'm really kissing up to these characters aren't I?). But if we did battle I would most likely lose. In my opinion she's the best of the Johto Dex Holders. And if she can ready my Pokemon for a capture, it wouldn't take much to switch out a Poke Ball for a finishing attack. So no, I wouldn't battle Crystal. Nor would I win.
Ruby: This will be a real shocker, I wouldn't neccessarily battle him either. Same reason as Yellow, he doesn't want to battle, and if he did, he'd go into "super serious, take after Norman, ***-kickinator" mode and I'd lose because he would put together both aggression and strategic moves. Ruby's battles are some of the most impressive for me. In his arc he seemed virtually unstoppable. So no I wouldn't challenge Ruby.
Sapphire: ... Okay, FINALLY! Yes, I'd battle Sapphire. She loves battles. And I also stand a chance as long as is doesn't come to her against me in a normal fight(how embarrassing to be nearly killed by a 12 year old girl, lol ^_^).
Emerald: Well he likes to battle too, so I guess I'd challenge him but I don't know how it'd go. I've only read a little af the Emerald arc(I'm still too busy to read the whole thing but I WILL get to it). So I don't know how the battle would go, but he beat the Frontier Brains, so I guess that's that. So I'd battle Emerald, I don't know who'd win, I don't even know what'd happen.
And I haven't even started DP so for Diamond, Pearl and Platinum, I think I'd just leave them alone. Besides I can battle the others off panel. I'd be in and out before anyone even knew I was there, with the DP guys, I'd get in the way of the plot since it's focusing on them right now.
So I'd battle: Red, Green, Sapphire, Emerald and maybe Gold. ^_^