Answer for question - Why did they "invent" Webdav
WebDAV stands for Web Distributed Authoring and Versioning
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Internet was just not meant for consumption of resources through urls (Uniform resource locator)
But that is what it became.
Because HTTP had strong semantics for fetching resources (GET) and (HEAD). (POST) provided coverage for number of semantic operations while (DELETE) was shrouded in distrust. HTTP lacked some other qualities like multi-resource operations.
In nutshell, it was read protocol and not write protocol.
You would go round about to make your resources (URLs) available for fetching by uploading it though FTP and many number of mechanisms.
WebDAV was supposed to provide the missing story of internet : Support for authoring resource through the same mechanism HTTP. It extended its semantics, introduced new HTTP VERBS.
It also introduced the mechanism to not only read, write, modify and delete a resource (uris) but also make inquires on the meta properties of the resource and modify it. It is not that you could not do it before but it was done through back door mechanism.
So you see, it brought some of the same mechanisms that you expect on file operations on desktop to internet resources.
Following are some of the analogies:
MKCOL ----- make collection ----- similar to make folder
PROPGET ---- get properties (meta?) --- same as get info or extended attributes on mac
PROPPATCH --- modify properties
COPY ---- cp
MOVE ---- mv
I hope , I have established some of the noble goals of WebDAV as extension to HTTP to support internet authoring. Not sure if we have achieved it though.
For your question
Your application is a client and will have to make do with what mechanism is available - FTP or WebDAV on the other side. If WebDAV is available great, you can use it. But It will take some time getting used to the semantics. FTP is has limited semantics and excels in simplicity. If you are already using it, don't change it.
Which is faster
That is akin to answering, which is faster HTTP or FTP?
On a sly note, if it was such an issue we wouldn't have been downloading / uploading files via HTTP ;)