LEDs are fast enough to follow the PWM signal. That is, there brightness changes from 100% LED intensity when the PWM is at 100% to something close to 0% intensity when the PWM is at 0%. Usually fast enough (several kHz at least) that your eyes do not notice, but a camera with a sufficient short exposure time will notice this anyway. Of course, you do want to avoid that.
If “Analog dimming” refers to the old dimming unit in AC circuits: they have the same problem, as they are working with chopping frequencies of 50 Hz (most of the world) or 60 Hz (US).
One way out is to have a truely analog current source; one way to implement such a thing is a DAC which drives a op-Amp paired with a beafy FET. An old schematic of such a setup can be found here.