As others have said - less dust showing in the print, more even illumination across probably any format size, focus remains stable (most of these cold lights have a heating element to maintain bulb temperature and performance), and highlights print more easily. Read up on Callier effect (no relation) for why this is so. And the contrast difference is not linear, so development adjustment is probably not really a perfect one, so contrast adjustments are probably needed anyway.
What I did experience when switching from condenser to cold light (at the time both were used with graded paper, so filtration didn't enter into things at the time-for me) was that I could add 15% - 20% to my film development time, to bring highlights up, along with better mid-tone separation. I looked at it as a way to increase tonal range in the negative.
I had heard about the "snap" thing too, but never saw it. Grain is also less pronounced, in my experience - a good or bad thing depending upon your "grain politics".