Very over simplified here, but let's say a stick and brick purchased for $100,000. Forget about tax, insurance, etc. Just the price tag.
Very decent Trailer at 50,000. Average 50 a night for 365 days is 18,250, for a total of 68,250. Leaving 31,750 for everything else to equal the 100,000.
I'd argue that 100,000 is pretty low for an average house, and 50,000 is probably high for a decent trailer. Gas, food, insurance, etc can eat up that 31,000 pretty quick, but that's just year one.
If you had 100,000 and zero income, you're done either way. If you have an income that'll cover monthly bills either way, the trailer wins for cost, but obviously loses big for investment. All depends on what you want out of it. Secure investment or life of travel.