How is K-1 quicker than CR-1 for citizenship?
Requirements are same for LPR who came under CR-1 or K-1:
1) Being married for 3+ years
2) Being LPR for 3+ years
With CR-1 you're already married when you file, so clock on condition #1 gets started earlier.
For condition #2, adjustment of status takes time. The time while waiting for GC doesn't count towards condition #2
CR-1 provides better protection for immigrant from multiple perspectives:
1) Travel bans make exceptions for spouses, but not for fiances
2) K-1 can expire
3) US citizens occasionally play games AKA "I changed my mind about marrying", "I cannot afford the fees" etc. And K-1 are more vulnerable to this.
As a foreign beneficiary, I'd feel a lot more confident with CR-1 being filed for me, and not K-1.
As a petitioner, I'd also be more confident about outcome with CR-1 compared to K-1 and to me it would be important to show real commitment (CR-1) and not a promise (K-1).
Finally, to many foreigners, traditional marriage back in their home country is important. CR-1 gives excellent opportunity to do this.
I'm totally aware this is just my opinion, and others may have valid reasons to go K-1. But I see fewer of these reasons in 2025.