Gif is by far the best algorithm for as seen above,
but there is a fly int the ointment..
to use gifs , the program you create them with has to have a licence from Unisys ($5000)..

If the program you used to create GIFs employs an unlicensed copy of the Lempel-Ziv-Welch compression algorithm, then Unisys says you are guilty of "contributory infringement" on its patent for the algorithm. Think of it as being an accessory after the crime. 
And this has been tested through the US courts in the favour of Unisys..