I've shot both, and from a technical standpoint it's very difficult to do talking to the camera well.
The first issue is that it's difficult for most people to have a conversation with someone they're not looking at. It's often hard enough just to get a person to have a natural, conversational tone when you're interviewing them face to face - making them turn and talk to the camera interrupts the flow of the conversation, forces them to focus on the fact that they're on camera, and tends to result in more 'performance' on their part. They'll also tend to glance over at you during the interview to check your reaction, and they'll generally turn away from the camera as soon as they finish a thought to see if you have a follow up question or response. This limits your editing choices - for instance, someone says something significant, you want to hold on their expression for a moment after they finish what they just said, but you can't because they immediately turn away from the camera.
The interrotron is an attempt to solve that issue - it allows the interviewer to have a conversation with the subject eye-to-eye, so they don't have to turn away, and helps them forget that they're talking to a camera and not a person.
The second issue is that it's very difficult to have multiple camera angles - which camera do they look into? It looks strange to cut between one view where they look at the camera, and one where they don't. If you only have a single camera angle though the edit becomes very difficult - if you want to remove sections to make things more concise (and you will) your only option is to have a jump cut (which looks bad in most situations) or cover the edit with b-roll.
For this video we used two cameras for the wide and close-up shots:
https://www.youtube.com/watch?v=JPgjHq4sjlU
We had to move the cameras as far back as the room allowed in order to minimize the angle between them. We got the lenses aligned as close as possible, with the wider angle slightly below the close-up camera (this looked better than having them side-by-side). We had them look into the close-up camera, because that's where their eyeline would be most apparent. It almost works - although the slightly lower pov of the wide angle is a little odd, and you can kind of see that they're talking just above the camera in the wide shots.
Now that 4k cameras are becoming accessible this is one of the use cases for them - shooting 4k, but delivering in 1080, means you can use a single camera to shoot a mid- to wide-shot, then crop in in post for a close-up. Combine that with a interrotron-style setup and you'd have the best setup for doing a talking to the camera interview - but if you don't need that from a creative standpoint it's going to be much easier to go with talking off-camera.