So, I tried to measure the black level
However, my instrument doesn't go below 0.01 Cd/m2, so I had to use alternative approach. I made a long exposure photo of the phone and my LCD monitor together and analyzed raw data from the camera to determine the black level (they are linear, unlike jpeg from the camera which is nonlinear and heavily processed hence not suitable for that). LCD monitor was set to lowest brightness. In that case it has white level 18 Cd/m2, contrast is 1:860 (determined with several measurements at higher brightness), so black level is 0.021 Cd/m2 (instrument shown 0.02) - similar to black level of UT30 plasma (just that white level is considerably lower because of significantly lower contrast)
First I set brightness of the phone to the maximum. In that case, black level is 0.0019 Cd/m2, while white level is 230 Cd/m2 for 100% white screen, or 290 Cd/m2 for 10% white and 90% black screen (obviously some power management used - like on plasma). Contrast ratio is 1:121.000 for pure white or 1:152.000 for 10% white screen.
By decreasing the brightness to 125 Cd/m2 (this was closest to standard 120 Cd/m2), black level slightly dropped, to 0.00166 Cd/m2. However, contrast ratio was almost halved
Quite decent for a mobile phone, although still short of marketed contrast ratio for even the cheapest LCD TV.
I attached a photo of first measurement below (it's intentionally slightly out of focus to avoid moire caused by interference between pixel structure of the screen and of the camera).
There are several things to notice. "Black" of LCD monitor has strong blue cast. Analyzing the raw revealed that its color temperature is more than 20.000 K, so I'm wandering why most reviews of LCD screens never revealed this big flaw of LCD screens - whether that data are omitted (in most reviews color temperature is shown from 20 to 100% APL) or are showing values around 9-10.000 K for 0% APL, and my monitor isn't the worst case, because it has CCFL backlight (LED televisions considerably worse) - in some reviews there is a sentence that shadows have slight blue cast and that's it ...
On the other side, "black" of OLED has red cast - color temperature is only about 1900 K. However, while blue tint of LCD is visible to eyes, this is too dark to perceive any color, at least for me. But very dark shadows (up to about 10% APL) also have red or yellow cast. Looks like this type of OLED screen has some problems with low levels of blue. Above 10% APL, color temperature of this screen is around 7500 K.
Another thing to notice is that this OLED has problems with uniformity of blacks, visible as dark dots or patches. However, I never noticed it except on totally black screen and wasn't sure that I see it even on black screen until I made this photo. On the other side, LCD panel itself has almost no uniformity problems with blacks, but however, has problems with non-uniformity of backlight, so it's certainly much worse
Black levels up to video level 19 are crushed - like on UT30 with default settings (however, there is no slider here to correct it)
Here is also a link to a page with similar measurements for some other mobile phones, two of them with OLED
Smartphone “Super” LCD-OLED Display Technology Shoot-Out
As a side note - my LCD monitor (Dell U2211H e-IPS) had maximum brightness 200 Cd/m2 when new, 1 year and 6 months ago. Now, it's only 145 Cd/m2. Contrast also dropped from 1:1200 to 1:860.