This question does to a degree solicit opinionated answers, but I feel it’s a good one nonetheless.
As far as my opinion goes and the way I handle things is this:
Definitely use the same handle for the same script in all your plugins and/or themes. You don’t want to load exact duplicates, if two of your plugins are used in the same WP install.
I give a generic handle to widely used and renowned scripts such as modernizr. Why should such a script be loaded more than once, under different handles?
I prefix handles of my own scripts, for reasons of namespacing.