Although typically a Fiancé Visa takes significantly less time to process than a marriage-based green card, due to the USCIS delays, the timeframe for both, is roughly 10 months. You can find the most recent processing times by visiting Historical National Processing Times.
While the K-1 Visa allows an applicant to reside in the United States temporarily, it does not allow its holder to work in the United States. There are other significant factors to consider when deciding which process makes sense for an applicant's particular situation. Please visit How is a Fiancé Visa Different from a Marriage Green Card? for more important information.