That's a good question willie ? From what I can tell the "Budd" style came before the " Dayton 's "
Just looking at WWII vintage trucks I see Budd type wheels .
I can't say for sure myself TD, both the Dayton Steel Foundry and Budd Corporation have been around since the early twentieth century, and I can't find for sure when either of the companies first made the wheels we know today. I do see reference to Budd Corp making wheels for military vehicles used in WWII, and I'd wager Dayton wheels were in use at that time as well because you can see many trucks of that vintage with the Dayton spoke wheels, I just don't know who did it first.
I can only speak for my area, but seems I recall back in the 60's and 70's, you take a B series Mack concrete truck with camel back suspension and the 46,000 lb rear axles they had the 6 spoke Dayton hub/rims. Same with the coal dump bodies mounted on DM or R model Mack trucks. I just don't recall seeing the heavy haul trucks in my area with Budd wheels back in those days, they pretty much all used Dayton hubs/rims. In my area I first noticed Budd wheels on OTR trucks.
And don't get me wrong, I have no problem with Budd wheels on an old B series like Truck Shop posted, not at all. I guess I'm just partial to the nostalgia of the old Dayton spoke wheels on a vintage truck, the spokes just exemplify the old school heavy hauler.