I am having this exact same issue and I cannot figure out the issue. I'm using an Elgato, Xbox 360 and Wii-U have same issue with HDMI. The audio stutters like crazy but at some random times during music it clears up. I saw a recent post here that talks about audio/video desync issues that started popping up around March 7th-9th, (which is when I started seeing a desync, and today the stuttering) and that a new driver for the elgato may fix it but has yet to be officially released. Although not everyone here has said they are using an elgato so maybe it was with a recent OBS update? I really wanted to stream this week but now I haven't the means to do so. Hopefully someone finds a resolve soon, personally I am now out of ideas. Here's my log in case someone needs it (sorry it appears to be too long, I have to link it):
https://gist.github.com/7fe2071b8e6d4f43a11c