I love the tape. ♥ I use Specialty Tape's double sided tape. When I used hot glue the ribbon just popped off after a few days, but with the tape it has never come off. One of my customers has a little girl who chews on everything including her hair clips and she told me that she never has a problem with her ribbon coming off compared to other clips she's bought before.
As far as the width goes, I think the explanation I've seen is that the 3/8" leaves a sticky edge on your clip and collects dirt and hair. I use the 1/4" and haven't had a problem with it. I make the ribbon on the back long enough to ensure a good grip so it doesn't lift up. If it's too short it won't hold as well.
This is only MY opinion.