Well, this question made me curious so I tried it both ways just now. I thought it was slightly easier to organize with LH quarters, but certainly playable either way. I'd do left.
However as Whynot said, there is nothing to stop you playing it with the right hand (why not? )
You may even not cross hands at all (although I believe that the crossing of hands is intended as an spectacular visual effect and one should cross them).
Here is something that Alexander Siloti said in an interview once:
I have a large hand, with a wide span, and do not need to resort to the necessities of small hands in playing. For instance, take the little Gigue in B flat, by Bach. It will be remembered that this short piece requires constant crossing of the left hand over the right, in order to bring out the melody. This effort is really not necessary, if one has a hand capable of reaching the intervals. I have altered the manner of performing the notes between the two hands, so there is seldom any crossing of hands necessary. In this way the piece is quite simple, and there is no change in the notes themselves. In fact the theme sings itself more connectedly through this manner of playing.
Best wishes, Bernhard.
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