Going for it on 4th and 6, if you miss it's likely an incomplete pass so they take over at the 47. They maybe take the ball back.
Punting they probably take over at the 10 or 20. Sure you can pin them inside the 10 but the odds of converting the 4th and 7 are probably about the same. Punting they almost certainly take the ball, except for a rare fumble or muff or something nuts happening.
Whether they take over at mid field or deep in their own territory doesn't matter. Once they have the ball back you either have to stop them on defense or you lose. The field position only determines at what position of the field they will be at when they are taking a knee and running out the clock.
All you really gain by punting is a few yards of field position when you're in a situation where yards are cheap and time is precious.
I'm sure these coaches know more about football than me or most other posters but sometimes you gotta wonder if they think some of the simple things through!