1) Size and dependencies. Let's say you want to use buttons directive. If you decide to go with angular-ui/bootstrap you will need this https://github.com/angular-ui/bootstrap/blob/master/src/butt... only - 62 LOC. If you decide to go with Strap you will need jQuery + 100 LOC of Bootstrap's JavaScript + 163 LOC of Strap's wrapper (!!!). Please note that the the wrapper itself is _longer_ than the original version. Native version is 1/3 of the size (!).
2) Customization - try to change a template for say, a typeahead. With the strap solution it is hard-coded in Bootstrap's JavaScript, no way to customize. With angular-ui/bootstrap template is here: https://github.com/angular-ui/bootstrap/blob/master/template... and is fully customizable
3) Integration with the AngularJS ecosystem - since anngular-ui/bootstrap directives are native ones they seamlessly work with all the AngularJS goodies like $q promises. This means that you can provide a promise as a source for, say, typeahead or data for modal.
4) wrapping existing jQuery plugins is not always obvious as lifecycles are really different. As the results you need to do hacks - just search Strap's code for setTimeout and $timeout to see what I mean.
At the end of the day just choose a project that works for you but we've started angular-ui effort since we believe that native AngularJS directives offer much lighter and cleaner solution.
angular UI version https://github.com/angular-ui/bootstrap/blob/master/src/aler...
strap version https://github.com/mgcrea/angular-strap/blob/master/src/dire...
It's not neccessary (bootstrap HTML is pretty straightforward) and it prevent you from doing a lot of things like custom html inside dropdown menus (icons, ni-click, etc).
So IMO, It abstract the things at the wrong level (too high)
Can you show us how they're wrong?