What is the best way to hide the joint between two drywall sheets (the framing is off on old house). Should I try and create a smooth rounded surface with drywall compound by building up both sides of the joint?
I'm working on the bottom side (of this drawing). It's old work, so Iwould like to avoid pulling down and changing the framing. Included from a comment.
You don't have a lot of options with your situation; you said:
Working on the bottom side. And it's not new work, so would like to avoid pulling down and changing the framing
The only thing to do is float it out, which like you were getting at means you build up mud on the face away from the point to make the point itself less conspicuous. Look up how to float out a high drywall joint or high spot on youtube and you'll find what you're looking for. Basically, you build up two lesser high-spots a ways out from the problem spot, one each side of the joint.
If you are up for it, blend into a heavier texture in the area. You don't want the area to pop out because of some crazy heavy texture, but a little heavier and it plays less noticeable with the eye.
Don't plane the drywall or shave it or anything like that. Once you compromise the paper, the gyp core will start to fail and ding easily and crumble out and then you'll be trying to shape it with hot mud or just replacing the boards anyway.
If you could get at the framing, you could adjust the plane of the stud in various ways or you can add joints in the field that help adjust the plane.
Good luck!
