Coming from a engineering\contract manufacturer's viewpoint, DOM is normally used for tight tolerance & clearance situations in assemblies. As previously stated, DOM is just the process to fine tune the tubing into a consistent, finite dimensional type of tubing. Any time you have either another tube or machined part going inside the DOM, there will be no interference due to lack of weld seam. If you've ever tried to install a weld bung in HREW, you know it's a pain in the ass. Same thing with square tube, as it's usually referred to as Telspar tubing (or no visible seam weld, i.e. hitch tubing).
The initial material type creates the standard strength, then the other processes just fine tune it dimensionally & yes, can make it stronger. I don't want dented up tubing in high contact areas, so I'm using a thicker wall DOM in those areas only. HREW will work perfectly fine for all other areas. I'm also using the thicker DOM in areas such as coilover & drivetrain component mounts, just for piece of mind.