At least for pixel graphics with transparency converting gif to apng would be a far better choice than gif to h.264 or vp9.
The thing is that you want 4:4:4 (no chroma subsampling) + alpha + lossless for pixel graphics. While some video standards support that in theory browsers often don't support those advanced profiles.
ffmpeg is not the issue here, it supports several 444/alpha/lossless codecs quite well, proes is not special in that regard.
Browsers only expose a small subset of codecs that ffmpeg supports. gif and apng are now the most compatible format in browsers for this kind of content.
FourCC of ap4x 'just worked' on IE (I might have installed QuickTime codecs), Safari, and gstreamer with Firefox - it just played in the window (though I did not test alpha channel). I was surprised too ;)
The thing is that you want 4:4:4 (no chroma subsampling) + alpha + lossless for pixel graphics. While some video standards support that in theory browsers often don't support those advanced profiles.