The difference may come from the fact that British people pout more when they enunciate words (I often think that British speaking requires more facial movement), where as Americans don't. With a word like this the difference may be minute and it may vary from region to region of America.
After reading difficult's reply, yeah, Americans do more of an -ee at the end.
In the U.S., it is generally pronounced ka-raa-tee outside of karate classes, even though it is fairly well known that in Okinawa it is properly pronounced ka-ra-tay. In fact, there is an often-played episode of the popular television show Friends in which the character Ross is ridiculed by his friends for pronouncing it correctly. (He was a very bad karate student, and no one takes him seriously about anything.)
It seems to me that Americans have a careless disregard for the origninal pronunciation of a foreign word when we appropriate it into English. I suppose that is because so few of us bother to learn a foreign language and we couldn't pronounce those words correctly if we tried. Once a word becomes widely used with an Americanized pronunciation, there's no going back.
MissFit, I have to say that British people are equally as guilty. My Austrian partner ridicules me for my poor pronunciation of such German words (accepted in English) as schadenfreude , Doppelganger , zeitgeist and etc, and my French colleagues look upon me with utter disdain when I attempt to pronouce French words accepted in English.