Disadvantages of dimming LEDs via current regulation as opposed to via pulse frequency?
This answer contradicts the assumption that constant current degrades performance for colour rendering. As far as the LED is concerned I assert there is no compromise using Constant current whereas PWM may cause "blue shift" from phosphor photon "quenching " OR insufficient dwell time ( two distinctly different phosphors and time sensitivities (Too long or too short. )

Phosphors for LEDs start with those typically used in traditional TV CRT's and Fluorescent tubes where used was UV to excite the phosphor for a fairly long time so that flicker at 60Hz would be less noticeable, thus the time constant of decay was in the 1~10 ms range.  Although LEDs use Blue as a substrate so phosphors in the blue range are not needed.  

Why is an LED white?

Think of White LEDs with massive thick transparent BLUE emitting substrate and a hundred atoms thick coated of phosphor that is critically thick to vary the colour from cool (thinner) to warm ( thicker).  Like some FL tubes they may be tri-phosphor for broader spectral and higher CRI quality levels which also affect other factors.


  The decay time &lt; shutter time causes the dark bands in the image.


The same phosphors were used in the Blue LED's with a very thin layer of phosphor which converts 10 to 20% of the Blue light into a smooth spectrum of yellow,green,red using yttrium aluminum garnet (YAG) phosphor (doped with cerium). The decay times are slower but the Red content was weaker, so mostly used in "Cool" white LED's.  This decay time is affected by PWM choices from 1k to 10kHz, where &lt;=1Khz may be noticeable on camera but > 1kHz might not and depends on both the PWM and the LED phosphor and CCT,CRI values.

Now with higher efficacy (>120LPW)  White LED's they have added more dopants to improve CRI as well with more red emissions. Phosphor selection will continue to evolve with quality indicators like CCT/CQS that also affect cost. They include oxynitride phosphors is the MSi2O2N2:Eu2+ (where M = Ca2+, Sr2+, Ba2+) compositions whose emission ranges from 575 to 675 nm.  

The phosphors are selected for cost, efficacy, thermal stability and longevity more so than response time, so PWM rates may have to increase for camera work or use filtered PWM.


  Filtered PWM has some losses associated with the real conductance or resistance losses in Chokes and Capacitors (ESR), but this is the most effective way to eliminate PWM flicker and may be added to any controller.  This is the same as the LC low pass filter (LPF) used in Class-E PWM audio power amplifiers.


For Linear voltage controlled current sources or sinks, there is of course the linear loss across the regulator.  This only becomes a disadvantage if there is a large voltage drop in the regulator.


Typically LED brightness range is limited by the quality or ESR of the power LED and thus the voltage range required from say 10% to 100% brightness.  In very high Efficacy LEDs this can be from 2.8V to 2.95V and in lesser efficacy LEDs, this can vary from 2.8 to 3.2V and worse.
Thus this range can be 5% to 12% (150mV/3V=5%,  400mV/3.2V~=12%). This implies the input supply voltage for the string must be buck,boost or series regulated to create this voltage drop to dim the LEDs and its pass current * voltage drop of 0 to 5% or 0 to 12%V * unknown I [Amp] implies the power loss Vdrop*I=P of this regulator, which can be quite good &lt;5% if well designed to match the string voltage +/-5 to 10%. This requires good DC-DC design principles with a desired response speed for modulated light with current sense and fast current regulated intensity.


Thus the PWM ripple current amplitude and time interval and the LED epiwafer phosphor decay times all affect the dark bands found in time aperture captured images.


  To prevent flicker the current ripple must be reduced, as the sliding shutter capture method may alias or interfere wit the PWM dead time from phosphor decay, when PWM is used. A line filter may be used to match the current peaks used with sufficient attenuation of the PWM frequency being 20~30dB or more depending on the camera image quality desired on grey scale background.. 


Linear or filtered PWM is the ideal way to control LED's to prevent the issues associated with diode saturation, efficacy loss, colour shift, but adds a little cost with the LC filter depending on quality and depth (-dB@1kHz) of the filter., (similar to an AC line filter cost)

There are also phosphors designed for LED photoflash that require a minimum of 50ms duration for optimal CRI, that may also reduce flicker effect with PWM.
http://www1.eere.energy.gov/buildings/publications/pdfs/ssl/chowdhury_phosphors-panel_sandiego2014.pdf