Need soundproof: Changing interior hollow core door to solid core, or exterior door?
First, "soundproof" doesn't exist. What you want to do is reduce the sound. In particular, you want to reduce specific sounds (conversation).
There are two kinds of sounds in buildings.
1) air born.
2) structure born.
The second, you can't stop with a door. Examples might be hitting the wall with your fist -- it vibrates the studs, the studs vibrate the other side of the wall, and the sound comes out.
So what's happening, in part, is your voices are going down the hallway, and then under and around the door.
It doesn't matter what kind of door you put up, if you leave air gaps under and around it.
Some of the sound that's going down the hall also strikes the door, and is transmitted through it (becoming structure born for a moment). A more solid door will help stop this portion of the sound.
I got a door for my practice room made by Masonite. It's designed for sound mitigation. I think it was over $100; maybe over $200. It works, but I installed it so that it closes really tight. You can also buy solid doors at Habitat for Humanity resale stores for a lot less. Exterior doors can work well too. But again, only if they close tightly on all 4 sides.
Note that if your room has a heating duct into it, that:
a) Sounds travel through duct work just as easily as under doors, if the runs aren't too long, and
b) If you seal the door, and if your room doesn't have a separate return in it, then you will have sealed off the return path, and the room will neither heat nor cool when the door is closed.
So a good first step is to put felt weatherstripping on three sides, and a rolled up heavy towel on the bottom, and see if you still have a problem. If so, go from there.