They are semi-competitive projects. At some point there were talks of combining 2 projects into one under https://github.com/angular-widgets . But guys have failed to agree on core architectural decisions.

Personally, I've started with with UI-Bootstrap, but then started to migrate certain components on Angular-Strap. The reasons was that some components like popover with template support were more functional in Angular-Strap. Also https://github.com/mgcrea/bootstrap-additions & https://github.com/mgcrea/angular-motion are nice side-benefits.

UI-Bootstrap development is not as active as it used to be.