I do pronounce them differently.
Gwenith has a "gwen" sound at the beginning (like Gwenodolyn) so GWEN-ith
Gwyneth has the Y sound in there so I say "GWIN-ith"
I prefer
Gwenith because I prefer
Gwen as a nickname to
Gwyn. Also the Y gives it a trendy feel (even though it's not a trendy name at all)