This fight would be tough because both have advantages and disadvantages. Both Godzillas devour radiation so their atomic breathes would hardly work on one another. Physically, Godzilla 2014 is superior but Godzilla 2000 is faster. At the same time though, Godzilla 2000 seems to have a style of charging blindly into battle to scratch and bite his foes. Godzilla 2014 has a different style as he tries to pin his opponents to where he can easily batter them to death and on top of all that, Godzilla 2014 also learns from his opponents and forms new strategies to counter them (for example, Godzilla eventually realized that the Flying Muto always attempted to flank him from behind and to counter this, he led the Muto into a trap by making him think that he was caught off guard and slammed him with his tail)(The second example being when Godzilla used his atomic ray against the Land Muto but since she was resistant, he later came to the realization that he had to destroy her from the inside). I know that many fans believe that Godzilla 2000 tried to destroy Orga from the inside but... he honestly could have just fired his ray down Orga's large mouth from a distance and easily have won the battle without being swallowed so... again, I don't think that was strategy, I'm pretty sure that was Godzilla 2000 just being... well, kind of dumb to be honest . While it is a close one to call, I have to agree that Godzilla 2014 would be the winner mostly due to the fact that he learns from his opponents' strategies and if Godzilla 2000 was to fight Godzilla 2014 at close range, he would be beaten to a pulp beause he would eventually be pinned and battered to death .
"Size matters not." The Japanese Godzilla has the advantage of having true atomic breath while the American version has atomic fire. So aside from being a bigger target maybe his thicker armor will provide some protection, but it's a coin toss to see who throws the first, possibly decisive punch.
As much as 2000 is my favorite design, I'd have to go with 2014. I believe he would win because of his fighting style: Brutal. He brings the attack to his enemy's and has armor protection. Good luck 2000!