FLV vs H.264 vs WebM: A brief description about each format
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Is a video format older than the H.264/MPEG4; it was used (and is still used) to distribute videos over the Internet through the Flash player, for this reason, it quickly became popular and turned into the standard for video distribution over the Internet. However, it is a format that in its beginning was based in a proprietary variation of the "old" H.263 (Sorenson Spark). Flash Player 8 made it possible to use a new kind of FLV, this time based on the On2 TrueMotion VP6 technology, that allowed to achieve higher quality videos at the expense of requiring more CPU power.
A format with no future
FLV has become obsolete and is rarely used today. It is strongy recommended to use H.264.
Is the compression technology behind the MPEG4 format, this new format produces higher quality videos and smaller sized files respect to other compression technologies. It is the compression format most used today and it is the standard for distributing high definition (HD) content. But the quality has a price: in order to encode and decode H.264 videos it is required more CPU power, this means that old PCs can have troubles playing back (smoothly) video files encoded in this format.
With the introduction of Flash Player 9 r3 Adobe started supporting the H.264 format, and the new F4V was born. The F4V is just a video file encoded with H.264/MPEG4 technology and "encapsulated" inside a file with .F4V extension; this opened a new world of possibilities for distributing high quality and high definition videos over the Internet.
A format for the present and the future / HTML5
The MPEG4 (H.264) format is the preferred video format to use with the HTML5 standard and, of course, with Flash. Compressing videos in this format guarantees the best quality and compatibility between technologies and devices.
Is an open video format, sponsored and developed by Google, intended to be used (mainly) with HTML5. Altough the format has been widely promoted by Google as a replacement for the propietary H.264, it has turned to be the H.264 format the one that seems to be "winning the codecs war" and is widely supported by most devices and Web browsers. In fact, Mozilla, who announced some time ago that they will not support H.264 in Firefox, in its latest mobile versions has started to support it and for the next desktop versions it is possible that the supports arrives.
The MPEG4 (H.264) format is the best bet and the most compatible format, in fact, this is the format we recommend. However, you can study the possibility to use (additionally) WebM for a maximum HTML5 compatibility, at the expense of more work on your part because of the required extra video encoding work.
Wikipedia: H.264/MPEG-4 AVC
Wikipedia: Flash Video (FLV)