Just on the fact that it's important for him to travel means you should definitely go for CR1. K1 plus adjustment is cumbersome, annoying and he will most certainly go insane not being allowed to leave the US. K1 and adjustment of status are also separate processes, meaning separate fees for both, meaning a higher grand total when you add it all up. CR1 is a much more efficient process on the basis that it automatically makes the immigrant a green card holder/permanent resident upon entry with the visa.
Every couple has their own priorities, and each couple must decide which visa is better for their situation.
K-1
More expensive than CR-1
Requires Adjustment of Status after marriage (expensive and requires a lot of paperwork)
Spouse can not leave the US until she/he receives approved Advance Parole (approx 6-8 months)
Spouse can not work until she/he receives EAD (approx 6-8 months)
Some people have had problems with driver licenses, Social Security cards, leases, bank account during this period
Spouse will not receive Green Card for many months after Adjustment of Status is filed.
A K-1 might be a better choice when 18-21 year old children are immigrating also
In some situations, marriage can affect certain Home country benefits, making a K-1 a better choice
A denied K-1 is sent back to USCIS to expire
CR-1
Less expensive than K-1
No Adjustment of Status(I-485, I-131, I-765) required.
Spouse can immediately travel outside the US
Spouse is authorized to work immediately upon arrival.
Spouse receives Social Security Card and Green Card within 2 or 3 weeks after entering the US
Opening a bank account, getting a driver's license, etc. are very easily accomplished with GC, SS card, and passport.
Spouse has legal permanent Resident status IMMEDIATELY upon entry to US.
CTCR reacted to Redro in K-1 vs. CR-1 for U.K. Immigrant