MKV does not play on iPhones, in QuickTime or in most browsers and editors. Ogg is open and royalty-free, which game engines and open-source tools favour. MKV is at home in films with several audio and subtitle tracks; OGG is the usual choice for royalty-free audio in games and on the web. The OGG contains the soundtrack only; the picture is dropped.
The defaults suit most files. Under Options you can choose the bitrate 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.
The conversion uses your browser's own video and audio codecs (WebCodecs), with hardware acceleration where the device has it; the file is read from disk as it goes and can be up to 2 GB. Where the browser lacks a codec, the page falls back to the compatibility engine. OGG is written at 160 kbps unless you choose another bitrate.