If I weren't in a hurry, I'd take the four-hour connection.

The possibility of a bus in DOH (or even a bus for each flight), security check again, a north-to-south or south-to-north transfer, etc., I'd just go with the long one and kick it back in the lounge. I used to find being in the lounge a bit disruptive to my work/play schedule, but these days, internet and the like are good enough that I can do almost everything I want to do in the lounge.

If you can't spare the time, obviously that's a different situation.