This is a situation that I've often thought through. I've also discussed it with my young bride, in the event either of us, or another family member, were the hostage. In both scenario variations, cooperation and timing could make all the difference in a succesful and disastrous outcome.
As Ex and others have said, there's simply no choice. Either the perp gives up or he gets shot. I will not give up my weapon or allow him to leave with a hostage.
As to the scenarios:
1) I'm very confident in my ability to hit the target at 10 feet with my 1911 primary carry weapon. When I'm convinced there's no other option I take the shot.
On the other hand, if I'm caught in this situation (shame on me!) with just my BUG, that's another kettle of fish. I'd have to advance and keep advancing until I'm in VERY close proximity or my hand is forced. There's still no choice but to shoot, at some point, however. Again, giving up the weapon is not even on the table.
2) Shame on me for carrying a weapon I've never fired, but there you are -- it is what it is. Considering results I've had with some really fine weapons on the first shot I've ever taken with them, I'd take the shot at 10 feet. It's a gamble of the highest order (as is the whole situation), but the alternative is so much worse.
It's always important to consider what can happen, not just what might happen.