Godlike
Cidolfas Orlandu (FFT) vs. Purim (SoM): Purim has spirits helping her...but Orlandu is considered one of the strongest warriors on an entire continent, and has far more experience on his side.
Geshp (SF2) vs. Zog (BoF1): Something tells me the king of the Dark Dragons in a Breath of Fire game ranks higher than a Greater Devil in Shining Force...this is mostly kneejerk though.
Odd Eye (SF2) vs. Altima (FFT): MEANWHILE, I think its easy to say Greater Devils and Zodiac Beasts are somewhat similar in power...and Altima's suppose to be somewhat on par with Zeon whose far more powerful than Odd Eye...yeah...
Magus (CT) vs. Myria (BoFs): Myria's being a Goddess is something she's actually proven worthy of in a few ways (the fact that she pretty much separated the entire world and held off an entire desert from spreading and controlled said world for 500 years...yeah...), Magus just can't compete with something like that.
Heavy
Emily (S3) vs. Alena (DW4): Emily gets actual hype for her strength and such, Alena kind of doesn't.
Zeno (BoF5) vs. Knight (FF1): Sheldar is a world where Strength = Everything, and what not (that's what D-ratios means, really) and Zeno's a pretty respectable rank. FF1 Knight, meanwhile...FF1 PLOT and all that, Chosen Warrior can only go so far.
Nina Wyndia (BoF4) vs. Jaheira (BGs): I'm going on the kneejerk of Jaheira being an experienced warrior means more than Nina whose just some princess who gets wrapped up in an odd situation.
Maya Schrodinger (WA3) vs. Rose (LoD): Ok, Maya's got pretty bad ass plot powers...but then again, so does Rose. So when in doubt, I'm going with the character who terrorized the world for 10,000 years as the tiebreak.
Middle
Bowman Jean (SO2) vs. Warlock (S4): Warlock is suppose to be some powerful uber mage or something...Bowman is just a pharmacist who knows how to fight.
Jude Maverick (WA4) vs. Porom (FF4): WA4 Hypes ARMs to hell, this feels like it matters more than your usual Child Prodigy White Mage.
Mid-Boss (Dis) vs. Blanca (SH2): No real contest. Wolf vs. Guy who is holding back a good part of the game mostly to help Laharl grow, and is suppose to be one of the most powerful demons, etc. Yeah...
Belselk (WA) vs. Kukuru (AtLC): ACF states outright that Berserk is actually the most powerful of the Metal Demons when it comes to raw combat ability. Kukuru is...a priest who shows little actual plot power that matters.
Light
Rikimaru (S2) vs. Gadget Z (S3): When in doubt, go with the character who can turn into a giant voltronesque robot at will <.<
Mustadio Buranza (FFT) vs. Jin Uzuki (XS2): Jin's suppose to be this bad ass swordsman with lots of experience who can lead an army and what not, so bad ass he can do the cliche "Deflect Bullets with his sword" thing. Mustadio is a random engineer with a gun
Roy (S5) vs. Rufus Shinra (FF7): When in doubt, go with the character who has a shotgun and not a stick as his weapon?
Aeris Gainsborough (FF7) vs. Virginia Maxwell (WA3): Good thing this match is last, cause I'm going to rant a bit on it!
I'm going to be honest here...
Aeris has very little plot power whatsoever. Yeah, ok, she can talk to the planet, and she can use the White Materia. Except this means...very little. Yeah, she can ACTIVATE it, but that's about it; remember, she activated it, and it did nothing until the main threat she was trying to stop was gone (at which point, there was another threat available.) Think about that...she tries and utterly fails at something. She completely lacks the experience and frame of mind to use said power. FURTHERMORE, Holy is completely useless against things the world doesn't deem evil (and considering Virginia's ideals are pretty pure and her actions to match...yeah...), I don't see how that would help her.
MEANWHILE, the Mediums in WA3 are something the game hypes are being incredibly noteworthy, and Virginia is one of *4 PEOPLE IN THE ENTIRE PLANET* that can actually use them, and she makes use of them as well. Combine that with actual experience in a deadly weapon (no, a pole is not a deadly weapon), and how as Elfboy said, Materia is used by everyone...yeah.
Also, FF7 never actually states Aeris is the only one who can use the White Materia, IIRC. Its just she was the one in possession of it, and having spoken with the planet, only one with something close to knowledge in using it. Seriously, think about it; if she really had full control over it, would she have said "I have materia, but its special; its completely useless!", and wouldn't it have, you know, actually activated and stopped the exact thing she was trying to stop?
So in the end, Holy might be that damned awesome...but Aeris very clearly had little control over it. To give you an idea, she has less control over Holy than Ex-death had over the Void, a power that eventually ATE HIM UP. That's not something I'm willing to respect.
Edit: And CK also reminds us that Aeris needed days to power that up...Virginia can access a medium and its full potential at any given moment. Its like claiming Sephiroth can blow up a planet at will...when it took him at least 2 weeks (excluding the 5 years it took him to prepare) to pull that off.