I just moved from owncloud 9.0.4 to nextcloud 10 and I face a very similar issue as in Davdroid no longer works with NC. I created another issue because 579 is solved.
I use davdroid 1.3.1-ose on Android 5.1
Everything works well on web interface and with ligthning on my thunderbird but I am facing this 503 issue (see 579 support ticket) on my mobile phone (and on my wife’s mobile phone as well) since I adopted nextcloud 10. Owncloud webdav client still works well also.
Here is the log : http://cxg.de/_4f35e0.htm