Which Michelin tires and which Firestone tires? There are at least two tire lines from Michelin in that size (and E load rating), at least three from Bridgestone-Firestone. The different tire models are designed for different applications although all have the same capacity.
Not completely happy with the LTX M/S Ford puts on the chassis when building it for RV makers, I chose slightly more expensive (and about 30% heavier) Michelin XPS Rib tires. But the LTX M/S2 does fine on my E-350 passenger van.
Bridgestone-Firestone equivalent to XPS Rib would be the Duravis R250 at about $240 per tire.
The bargain commercial tires from Bridgestone-Firestone are the Duravis R500 and the Transforce HT, at about $170-$180 per tire. Michelin does not sell a commercial tire at this price point using the Michelin brand, the equivalent Michelin tire to a Transforce is BF Goodrich Commercial T/A.
Both companies also sell bargain commercial truck tires (Destination, Long Trail at $100-130) in our size, using their BFG and Firestone brands.
They also sell SUV/Light Truck tires for passenger service, e.g. Michelin's LTX lines and Bridgestone's Dueler lines. Certain models of these softer riding, quieter tires are built as Load Range E in 16 to 18 inch sizes, for 3/4 ton and 1-ton applications, because so many trucks and heavy SUVs are sold as passenger cars, and buyers don't like some of the NVH compromises that come with the longer wear life of commercial tire designs.
Go over to Goodyear-Dunlop-Fulda and you will find the same thing, premium commercial tires around $230-250 (G947 Armormax), mainstream passenger/commercial tires under $200 (e.g. Wrangler HT), and lower cost models for urban delivery where high speed driving is not as much a design factor as handling bouncing off curbs and hitting potholes.
So if you compare one company's best tires to another company's cheapest tire that fits, you will see a price difference of about 2:1. I think you are probably comparing two different classes of tire, not two different companies.
If you don't do a lot of highway speed driving at high temperatures, a cheaper tire can save you some money, because RVs do not usually put on enough mileage to take advantage of the longer wear life of high-end commercial tires like the Armormax, XPS, or Duravis R250. U-Haul does quite well with Wrangler HT from Goodyear, Transforce HT from Bridgestone-Firestone, and Michelin's BFG Commercial T/A. They even mix the brands on any given truck.