I am considering the Hampt0n Bay or the Litex outdoor ceiling fans for our breezeway,
Which one is the best?

Both of these brands are pretty terrible. Hunter, Casablanca, Emerson, and Envirofan all make much better fans. Some are in the same price range, some are more.

Of the two brands you mention, Litex/Harbor Breeze is slightly better than Hampton Bay.

Ceiling Fan Brand & Manufacturer Recommendation - Ceiling Fans N More