The only "big" difference it makes is to the look of the move - the advantage of bending the inside leg is that it is 'hidden' behind the outside leg, so you don't compromise the visual leg line.
The other significant difference I see is that if the man needs to control the lady's balance, it is more likely that he'll have to do that by providing extra 'lift' via her right arm. For a lot of drops this is harder than if he were providing lift via the left arm. (I don't think this is actually a big issue if the man's reasonably aware of the balance, but if he isn't, it might be).
For the same reason 1-armed drops (which usually use the lady's right arm) are often actually easier to control if the lady bends the outer leg, although they still look better if she bends the inner one.
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