Who cares about the rise/fall time of the PWM?
Humans can perceive flicker up to a couple of kHz at most. Therfore you don't get any useful information from that.
So being able to measure from DC to 10kHz is enough, maybe up to 100kHz if you interested in the actual PWM frequency.
So even cheap photodiodes with a nearby amplifier should be fast enough for that job. Phototransistors are typically too slow.
As already shown, the signal measured can be difficult to analyse if you don't have full control over the backlight PWM.
I did some quick measurements using a OPT101 (14kHz BW) and another photodiode+amplifier (~250kHz BW). The OPT101 is much more sensitive than the other sensor and therefore better suited for the typical brightness from a display (that does not mean you can't get a fast sensor with a high BW, but it gets more difficult if you need both, because at some point you end up using a photomultiplier tube).
OPT101:
250kHz sensor:
As you can see the waveform measured using OPT101 has the same shape as the other signal, but it is missing the high frequency contents (double the operating frequency of the CCFL). The lower frequency is the 180Hz PWM frequency (3x framerate).
This is the light output of the CCFL.
Let's say you want to measure the response time of the display, this would be difficult with this signal because of all the other frequencies and the PWM signal masking the wanted signal. To get rid of the PWM signal, I did set the brightness to 100%, ac coupled the signal and applied some filtering to remove all of the CCFL operating frequency. I have no idea why the waveform looks like this, maybe the monitor can't do 100% PWM but only 99.9% or so, producing a small spike. But you can clearly see every 3rd cycle looks different.
Looking at the frequency spectrum we can clearly the the peak at 91.5kHz and half of that at ~46kHz. The small spike at ~66kHz could be ripple from the main SMPS. But except from that there is not much else interesting to see above a couple of kHz.
If we zoom in, we see spikes at multiples of 180Hz. Hard to see here, but with a very long FFT (>1M samples) we can see peaks at 30Hz and 60Hz showing the actual flicker of the TFT LCD. I can also see a small spike at 15Hz. That could be dithering because the TFT panel itself probably is 6bit and is expanded to 8bit using framerate modulation.
That's why I suggested using a PC based scope or a scope with a good PC interface for downloading the samplebuffer for further processing, because the built in FFT in most low end scopes isn't good enough for high resolution FFT using the full sample memory length.
You can do many different measurements on displays using optical sensor and get lots of information from that, but interpreting the results can be difficult.
Typical photodiodes have a peak resonse in the near IR, but that is ok if you only interested in changes of the brightness.
There are photodiodes with an additional filter to match the response of the human eye, but since they filter out light, the sensitivity is lower and they are more expensive.
If you care about absolute brightness or colours, there are also calibrated colour sensors, but they are even more expensive (you can easily spend >100k on optical measuring equipment for displays).