Both of my grandmothers were avid quilters; one did ALL of her quilts this way, the other did NONE of her quilts this way. I possess quilts of both type that have been used and loved for years, and I don't notice either style of binding being more durable than the others - the fabrics and the use & care of the fabrics seem to be the really important factor. I notice quilts I used most on my bed as a teen have the worst binding along the shortest edges - I'm assuming that's from my greasy teenager face touching the binding there the most!
For my own quilts, I do some the "flip over" way, some the "separate" way...depends on the fabrics, the quilt, and my mood.
Thinking about my quilts, I think I do the "separate" way about 80% of the time though.
I'm making 2 quilts for Christmas this year - one will be bound the "flip over" way, the other will be done the "separate" way.