Why the codec matters
A remote-desktop session is, in effect, a live video of the remote screen. The codec compresses each frame so the stream fits the available bandwidth, and the viewer decodes it again. Screen content is unusual video: long static stretches, sudden scrolls and text that has to stay sharp. The better the codec, the sharper the image at a given bitrate, which matters most on slow or congested links. Better compression usually costs more processing, though.
The four codecs
H.264, the ITU-T's Advanced Video Coding standard, is the most widely deployed of the four, and most GPUs can encode and decode it in hardware. VP8, whose format Google documented in RFC 6386, is light to encode in software. VP9, the WebM Project's next-generation open codec, became available in June 2013 and compresses better than VP8 at a higher processing cost. AV1, the Alliance for Open Media's open codec, compresses more efficiently again; for real-time use it is best encoded on a GPU that supports it.
How Vexaro Desk handles video
Vexaro Desk adapts the stream to the machine it runs on: it makes use of the hardware where it can and needs no special GPU, and any Windows client can display every session it receives.
While a session runs, quality and bitrate adapt to the link, so a degrading connection lowers the picture quality instead of freezing. On paid plans operators can switch between quality presets.