I think it looks fine.

I must be missing something, I have studies both pictures and think the both look fine.

I think both ways look fine. One thought I had was that perhaps the back looks better to you since it matches the backing. Could that be it?

For machine binding, I used to sew to the front and turn to the back and stitch in the ditch, but recently tried sewing to the back and turning to the front and using a decorative stitch to stitch in place and really like how it looked. Usually cut 2-1/2"

For stitching the binding in place by hand, I do prefer the look of stitching to the front by machine, and stitching to the back by hand. Usually cut 2-1/4"