I personally like Jasmine better, mainly because the name generally gets shortened to Jazz anyway. Jasmine looks much more feminene and soft, the other looks odd to me.
That's what I reckon - the softness, in the way it's written... I love words and how they appear and so the spelling is very important to me (drives M mad )

Maybe that can be my compromise, because I'm fine with "Jaz/Jazz" as a nickname. I've got a bit of time up my sleeves, anyway. Who knows, I got my way with T's spelling!