Most WebDAV servers do not support preserving timestamps, when uploading files. So any kind of synchronization against a WebDAV server will always be limited. But to some degree it might still work. I cannot be more specific without more details from your side.
See also https://winscp.net/eng/docs/faq_synchronize

I have a litte script, which uses put and get with option -neweronly.
It puts the local file to remote, if local file is newer than remote file and it gets the remote file when remote file is newer than the local file.
This works fine with FTP.
But it seems it does not work with Webdav.
Because it always puts the local file and always gets the remote file.
Any suggestions?
Thanks.