Why is there such a vast difference in refinishing quotes?

I have 2 floors. 415sq ft and 215sq ft I’m looking to refinish, no stain. So far I got 2 quotes. 1400$ and 6000$. I asked the 6k company why their price was so much more. They said they use better material and put more care into their work. 6k seems expensive and 1400 seems cheap. I don’t know much about flooring, quality of poly or concerns to have.

I do have a 3 year old 60lb dog so I have a worn area by the back door. Would it make sense to do it cheaply now and revisit a more expensive option once I no longer have a dog.