Uproot and Awkward Array both have Zenodo badges, which link to a page that has a lot of ways to cite the software (copy-paste to BiBTeX, etc.)
The papers are conference proceedings that emphasize different things, not all of which are the software itself. (One of them covered user feedback in a series of interviews, very different from a design document.)
New versions (including Awkward 1 and Uproot 4, after the name swap is done) will be added to the same sequence, so if someone follows one of these DOIs to its Zenodo page, they'll find cross-references to newer versions. So all in all, I think this is a better way to cite them.