Welcome! I have not used exist, but I can share my history. I used sedna for many years. When development stopped I looked for alternatives. I have read many comparisons in WWW andI have found basex.

A detailed benchmark of basex and others: https://bbddxml.wordpress.com/2014/01/08/un-benchmark-para-nuestras-bases-de-datos-xmark.  If you know xmark, it is most important and most cited benchmark for xml. I have run these tests also (for Sedna and basex), and published results are close.

In basex I notice that writing xml result to files is very fast. Also query and indexes optimisation is very clever (pues, more clever than me), sometimes only few miliseconds for gigabytes of xml. And basex has excelent support for official w3C standards (Fulltext, Update, all of Xquery 3.1. see https://en.wikipedia.org/wiki/XML_database). And very stable.

I have used berkeley in early times, it was very slow.

One question to the team: Can you include replication feature?

Best regards Julio