Both the K-1 and CR-1 will take about the same amount of time before you can live in the US. With a CR-1, you can start work immediately after entry into the US with the visa. With a K-1, you would have to enter the US with the visa, marry, file for a Green Card, and wait about 6 months before you can work. Among other reasons, if working sooner is a priority, then I would eliminate the K-1 completely.
With a CR-1, you receive the Green Card almost immediately after entry. With a K-1, you could be waiting a year after entry for a Green Card.