It's still the case that AVI & MPEG4 (HD or not) are containers, whereas h264 is just the video part, i.e. no audio. As far as I know, there are no true formats called HD-H.264, HD-MPEG4 & HD-AVI. I'd imagine that the HD prefix just means that you'll retain blu-ray image resolution and possibly audio quality.
So you still need to find out what video & audio formats those options include and also you'll need to check what your TV or blu-ray player (I'm assuming you'll be playing them on one of these as you're in this forum and talking about HD) can accept. Or you could just try a disc converted in the various options and see what works for you - there's a lot of personal preference when it comes to video & audio!
I use DVDFab and rip my blu-rays to AVI with h.264 video and AC3 audio (my TV - grrr - doesn't accept DTS or any HD audio). I could also choose the MKV container with the same video & audio, but for me there is no advantage in doing this.