The S Mini is slightly shorter than the Mini Mk II but Hogokansatsuken is right the difference is not significant. Of the two I carry the S Mini sometimes but not the Mini Mk II. The Mini Mk II has impressive output with the supplied li-ion but the UI doesn't work very well and the S Mini seems to be brighter when both are using primaries. I wish the Mini Mk II worked like the old Minis I still carry them frequently. I haven't tried the S Mini on li-ion but the output is supposed to stay the same (550 lumens). It will not give you the high output that the Mini Mk II can with its li-ion battery.
On a side note,the clip that comes with the Mini MkII fits the S Mini perfectly and is much better IMO than the S Minis original clip.