First, I have no financial interest in either of these two restaurants. A few reviews for both restaurants made me wonder if they had an interest.
I prefer single patty hamburgers compared to multiple patties so that is what I ordered at both restaurants along with fries and a drink. Mooyah sells milk shakes and Five Guys doesn't (I did not purchase one at Mooyah so can't say anything about the quality)
Five Guys: I have been here a total of three times. I purchased fries every time and burgers two of the three. I went there during the first several weeks that they were open and I think that most of us can agree that it would not be fair to judge them during that initial period. That first visit was for fries only.
I did not see any seasoning added to the burger at Five Guys. The meat was certainly OK, but the lack of seasoning was noticeable. The patties were more greyed than browned Both times my burger toppings were correct. I thought it was decent, but nothing to get excited about. For a single patty burger (not cooked to order), the price seemed a bit high at more than $4.
Fries: I ordered both cajun and regular for all three visits. One of the orders of cajun fries was simply awesome--crisp fries with the proper amount of seasoning. The non-cajun fries were either underseasoned or undercooked or both.
With only one order of fries, single burger, and drink, the total was over $9.
Mooyah Burgers: 2 visits. They offer a few more toppings than Five Guys for what that is worth. Both visits the burgers and toppings seemed "to meld together". I could not see if the patties were seasoned, but they were more charred than Five Guys (which is my preference).
Mooyah Fries: First visit, the fries were nicely crisped, but I watched the guy take them out of the fryer and put them with my order without any seasoning (which is so wrong). They have a container of their fry seasoning available at the counter which helped (fries immediately out of the fryer, should have seasoning applied as soon as possible. Second visit the fries were great crisp and seasoned to my satisfaction. I could be wrong, but I think with a drink, single burger, and fries; the order costs somewhat less at Mooyah.
While certainly not a scientific study, for me Mooyah stands a little higher on my preference scale