It seems to be 3 different forms to Takuma.
There is Takuma
http://www.vesta.dti.ne.jp/~tsato/cg/xvi_takuma.jpg
were he is not fighting at his full capacity or holding back. (He is as strong as Ryo, or Terry if you want to compare)
Mr. Karate
http://bohyou.vis.ne.jp/neogeo/aof/eban01.jpg
were he now unleashes the full power Kyokogen ryu. Mr. Karate has made very few appearances, the few times he did he was the end Boss or a secret boss in SNK, well up until SvC chaos
(He was the final boss in Art of Fighting 1, Ryo was the secret boss in called Fatal Fury: Wild Ambition)
I would safely place him along the ranks of end bosses that achieved their power thru dedication and natural talent. - Some ware along the lines of Geese, Kruaser, normal Rugal etc..-
Honki Ni Natta Mr. Karate (or "Serious Mr. Karate"

this is the latest incarnation of Mr. Karate. Here in the cross over game. Snk separates Mr. Karate and Serious Mr. Karate.
Unlike Mr. Karate ware in the canon plot line the mask does not grant more power to Takuma.
In the Snk vs. CC the story seems to point out that it does. Granting Takuma deadlier than his alter ego Mr. Karate and seems to be as powerful as say Shin Akuma.
Art Of Fighting 2 Dialogue
Takuma
Before The Fight With Geese:
Geese's Bodyguard: Ms. Takuma Sakazaki? The police commissioner would
like a word with you. Could you walk this way?
Takuma: The commissioner? I wonder what this could be... a trap? Wah!
----------
Vs. Geese:
----------
Geese: Long time no see, Takuma! How is your daughter?
Takuma: Geese? You...!
Geese: People should learn to finish their sentences. But I'm happy you
remembered my name, ya... big galoat! Care to make up?
Takuma: I said it before and I'm sayin' it again... no, no, no! Okay?!
-------------------------
After Takuma defeats Geese:
-------------------------
Geese: Is this how you treat your kind benefactor? Oh, cruel world!
Takuma: Quiet! Now I pay you back for everything! Ha oh... eh! What the
heck...?
Geese's Bodyguard: This way, Mr. Geese.
Geese: I have lost this time, but I'll be back. For now my farewell!
Takuma: Wait, the battle isn't over yet, Geese!
SvC chaos dialogue
Geese Howard vs. Mr. Karate:
GEESE: What's with that ridiculous mask? Insulting me, Sakazaki?
KARATE: Don't know Sakazaki. They call me, Mr. Karate, the Karate Goblin...
GEESE: Imbecile.
KARATE: Yeah, but Mr. Karate's no ordinary imbecile... You'll see for yourself!
Geese Howard vs. Shin Mr. Karate:
S.KARATE: Who would've thought that young punk would be what he is today?
GEESE: I know you! Takuma Sakazaki!
S.KARATE: Don't you think you've gone a little over the top, Geese. Huh?
GEESE: Hmph! I'm not the kid I used to be!
Note
Geese was the real final boss in Art of Fighting 2
Mr. Karate was the secret boss in Fatal Fury Wild Ambition. It is later revealed that Ryo was posing as Mr. Karate.
http://www.snkplaymore.jp/official/nbc/character/img/p_karate1.jpg