I would think there would be a slight difference but very little and that would depend a lot on the operating frequency. Two quotes gleaned from Google and appear to be reliable sources:
"Litz wire is used to make inductors and transformers, especially for high frequency applications where the skin effect is more pronounced and proximity effect can be an even more severe problem. Litz wire is one kind of stranded wire, but, in this case, the reason for its use is not the usual one of avoiding complete wire breakage due to material fatigue."
"Litz wire conductors are beneficial for reducing A.C. losses in high frequency winding"
So this is just to make a point that Litz wire is used to improve effeciency, this would be especially so in SMPS like computer PSU's where the transformers operate at high frequencies. It's not used for inductance reasons as far as I am aware and probably makes little difference.