There's some hassle with either approach, I'd just say it's a different sort of hassle.
If I update, say, the X server in Gentoo, I can expect and be prepared for some problems with, say, 3D, but I still expect the kernel to boot, sound to function, etc.
If I upgrade the whole distro, all bets are off. Will the printer still work afterwards? No idea.
I don't know which approach ultimately costs more time, I just know from experience that I personally found the distro upgrades more frustrating than individual package updates.