yeah, another reason to use .ts or .m2ts over .mp4 is if you use a video editor.
when you record with the mp4 container, the video can result in variable frame rate. the video will play fine in software players which anticipate that the video might have variable frame rate instead of constant frame rate. But if you use video editors, they do not like variable frame rate videos at all. you'll end up with audio/video synchronization problems. This problem isn't restricted to the Hauppauge. I read details about it in other forums like Avermedia. In fact, all iPhone video is variable frame rate as well. With .ts, it will always (as far as I can tell) be constant frame rate.
I also use VideoReDo and their tech support says their product doesn't support variable frame rate. So my two big editors (Adobe Premiere and VideoRedo fail on variable frame rate videos.
Be advised is that if you work Handbrake into your workflow, make sure you choose constant frame rate as your option! Do not choose the variable frame rate option! Note that I'm talking about frame rate and not bitrate. Two entirely different issues.
I was hoping to be able to record in mp4 so that I could easily edit in Adobe Premiere since Premiere doesn't support .ts files. But that hope is dashed. I did read that this may be a function of CPU power and/or encoder power. As people who recorded MP4 videos at 720P were less likely to produce variable frame rate videos. It was mostly people who recorded 1080p30.
I think I agree on the use of Showbiz to record. I have a better sense of what it's doing (like what you said about information about the incoming audio).
If I ever need the live streaming (which I doubt I'll ever do this), then I know to use Hauppauge Capture. But it's Showbiz for me.