WebDAV is an older standard and is based entirely on the HTTP specification. In fact, HTTP was extended to move it from read-only to read-write. Before WebDAV the HTTP specification was not able to handle back-and-forth file transfers so it was extended for that purpose. WebDAV is very rudimentary and only lets authors manage in a file-browse mode. The first WebDAV spec that came out did not include versioning capabilities. It was later on in the "Delta V" release of the spec where complete versioning was spec'ed out. While WebDAV is extraordinarily prevalent (Microsoft desktops, some Adobe products, etc) most vendors have only implemented the earlier WebDAV spec. (i.e. not DeltaV)
CMIS on the other hand is a much more complete and rich specification. CMIS is basically a web-service based common API. CMIS includes support for extending metadata, searching, advanced permissions, versioning capabilities, etc and really further advances the notion of a common-plumbing layer for an organizations' various repositories. It is really a common denominator API amongst the various ECM vendors such as Microsoft IBM, OpenText, ECM and so on.
Volumes could be written on CMIS at this point but those are some big differences. One note is that of this writing CMIS is still not a 1.0 spec (almost there) whereas WebDAV had been around for over a decade. There are likely to be considerable changes coming as CMIS evolves.