MKV does not play on iPhones, in QuickTime or in most browsers and editors. OGV is open and patent-free, which Wikipedia and open-source tools favour. MKV is at home in films with several audio and subtitle tracks; OGV is the usual choice for open-licensed video on Wikipedia and Linux.
The defaults suit most files. Under Options you can lower the resolution, trade quality against file size, remove the sound and trim the start and end. This is demanding work for a browser: a long or high-resolution file can take several minutes, and your device does all of it, so keep the tab open.
This pair uses the compatibility engine, ffmpeg built for the browser, because OGV cannot be written by the browser's built-in codecs. It is a one-off download of about 10 MB that the browser keeps, it is slower than the built-in codecs, and it takes files up to 1 GB.