Bodybuilders tend to be weak as fark where it counts.....there are many exceptions, but your average douchey gym goer literally spends like 2 hours a week on direct arm work and basically is pissing time away in the gym while looking at chicks in yoga pants....
There is nothing wrong with it, but it is what it is, and I used laugh at those people.
When you say "weightlifting strong," what do you mean...do you mean people like those Dbags?
Do you mean people who use olympic lifting to increase performance in a sport where power is key?
Do you mean someone like me who was basically a powerbuilder in my 20s?
Do you mean clueless women who go in their and hit 6 machines circuits at 20 percent intensity for 25 reps every other day and think they are doing something?
CF is a fairly effective protocal because it often utilized olympic lifting, full ROM squatting, some dead lift variants and other BW exercises.....not because it's put together and structured the CF way.
That's basically my point. I am not shocked people who engage in CF are functionally strong, but I wouldn't rush to attribute that to some proprietary CF workout. It's probably the same reason Olympic lifters would be fnctionally strong- heavy front squats and push presses make you functionally strong.