I may be wrong, but I think DOM stands for "Drawn over Mandrel" a manufacturing process. DOM mild steel tubing like 1010 have about 30,000 psi bursting strength with 1028 having closer to a 70,000 psi bursting strength. DOM 4130 tubing starts out at 60,000 psi bursting strength and can be increases to 90,000 psi with heat treating.
There a lot of frames made from mild steel and there is nothing wrong with it. It is easier to bend and weld. 4130 is used a great deal in aircraft manufacturing where strength and weight are prime considerations.
Additionally, there is "Seamed" (ERW) and "Cold Drawn Seamless" and "Hot Drawn Seamless" types of tubing. Cold Drawn Seamless is very expensive and the best quality (though not needed for a bike frame).
I'm pretty sure that the NHRA requires the use of 4130 in Dragster and Funny Car Chassis construction while also specifing a minimum OD and wall thickness.
Cheers, Tom