There seems to be a bug in apple wireless direct link (AWDL). It causes stuttering when using airplay. I think the bug goes into el-capitan too.
To fix it, you can turn off AWDL, although you lose airdrop. A small price to pay to get streaming back, as well as improving wifi substantially as well.
To turn off AWDR type the following into terminal
sudo ifconfig awdl0 down
sudo ifconfig awdl0 up