I have used both, the only problem with super glue is that it makes the fiber brittle. So if the fiber won't be moved around, then us Super Glue, but if you are still working on bundling it I would use white glue.
Another thing to think about is painting. I would either paint in advance or let the fiber hang out about an inch or two so you don't have to mask it. If you leave fiber out and paint, then when you are done you can nip the end off , make a lens and then slide it back into the whole the a drop of glue behind the lens. It works great and you don't have to mask the fiber, the only problem is that you do waste a little fiber...