Transport streams do not play on phones or in browsers and are awkward to edit. FLV is still used by some live-streaming and recording tools. TS is at home in broadcast recordings and camcorder footage (MTS, M2TS); FLV is the usual choice for nothing new; it survives in old downloads and stream recordings.
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 FLV 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.