If the destination is your own website, an HTML <video> tag, or a CMS that accepts WebM, MOV is the wrong starting format. MOV is great for archive and editing (heavy, container-rich, codec-agnostic) and the opposite of what a web page wants. WebM with VP9 is built for that use case: lean container, efficient codec, native browser playback.
In practice the saved bandwidth is meaningful. VP9 often produces smaller files than H.264 MP4 at matched perceived quality, with the largest gains on natural footage like talking heads or landscapes and smaller gains on heavy motion. Exact ratios vary with content.
Browsers with a supported VP9 encoder can perform this conversion locally. Drop in a folder of MOV clips, set a width if you also want to resize for the web, and get back WebM files without uploading the source.