Drawboring is a fine technique. I'd view strap pulled joints as a shortcut, trying to achieve what is better done through offset peg holes. But that's my opinion. So I'd concur with the opinion that you should fit the assembly, mark the holes, then drill them offset by a small margin.
Using straps may be faster (if you haven't much practice) but does not work as well.
That said, some carpenters of the past were known to have used a Spanish windlass for just this purpose, which is a looped rope wrapped around two timbers with a stick between them. The stick is turned, twisting the rope and drawing the ends together. tremendous amounts of leverage can be gained this way, and it is a very useful device for closing particularly stubborn assemblies. Although, if an assembly is stubborn I personally feel as if the joinery should be adjusted until it fits better, not forced together with ropes and straps.
