I'm not familiar with "offset" welding. Are you talking like "a" (welded one side) or "b" (welded both sides) like this?
A flange weld would be like "c" here.
Obviously, the advantage of "c" for a lapped joint is that you have a flat plane on one side. If you're lapping the two pieces without a flange, you're never going to get it straight. There will be a change in plane that is going to give you issues. A butt joint would be similar to "c" without the lap - keeping the two pieces in the same plane.