Okay, thanks for all the comments. After all that testing, reading, etc. I grabbed a cheap TN monitor BenQG2420HD - they offered it with 33% discount to empty the stock, to make room for all the extra-hip LED panels. After a few hours of testing, I have decided to keep it. First, it does not strain my eyes like the LED ones. After gaming for a few hours, nothing. After the same time at a LED monitor, my eyes are red and full of tears.
The colors are noticeably inferior to the Fujitsu P23T-6P panel, but that is to be expected (CCFL vs LED, 6bit vs 8bit). However, the uniformity of the screen is noticeably better, the fujitsu has a strong purple tint to blacks and strong backlight bleed in the lower left corner. The TN panel, believe it or not, has much better blacks, and I think contrast overall too.
Response-wise, the TN panel is much better. I play one extra-twitchy game, Mount and Blade Warband, and all the super-fast sabre and sword duels when you must block precisely in the right direction put any monitor to a very rigorous test. On Fujitsu, it is unplayable, the moving objects are not fluid, they jerk visibly, and everything has a strange stroboscope-like quality.
I have realized a maybe important thing - our eyes are comfortable with blurred movement in incandescent light (sunlight, candles, tungsten lightbulbs). Because the light is continuous, the moving item reflects it in every moment of its path, creating a continuous stream of visual information, a blur that the brain is capable of processing - that way, you can catch a ball, block a fist, or dodge a thrown stone. It all happens on a low-level of processing where rational thinking is too slow - that's why sportsmen and fighters must train their low-level reflexes by repetitious drill. That we can do - it's our heritage from a species fighting for survival for thousands of years under the incandescent sun- and moon- light.
However, if you substitute the incandescent light with a flickering fluorescent light, The stream of information in form of reflected light ceases to be continuous - you receive a certain number of discrete "snapshots", and the longer is the darker period of the PWM flicker, the fewer snapshots you get. Note that while movie frames that contain the "blur information" seem quite fluid at 24fps, we need at least 60fps of discrete, sharp-edged computer generated images to achieve a sense of fluidity. Now if you skip some of them due to the dark phase of the PWM flicker, you create an even more disconnected set of discrete images the brain has more trouble to interpret and extrapolate - it's no longer a blur.
The CCFL backlightflickers too, but because it stays on a few milliseconds after the current is switched off, the effect is less pronounced - the dark period of the PWM flicker is shorter, with less steep edges. LED switches on/off almost instantly, so the flicker is more noticeable, and requires higher switching frequency to become less bothersome. The manufacturers, to save development costs, use the old PWM circuits calibrated for CCFL use - and what was okay there is IMO grossly insufficient for WLED. They may change their ways, if there is enough discontent among the customers, that remains to be seen.
Does anyone knows if AMOLED displays are dimmed also by PWM, or by current levels? Could they mean salvation for our weary eyes?
BTW there is a battle going on between the regulators and LED bulb manufacturers (general lighting) for the minimal switching frequency required when dimming.
Energy Star pushed 150Hz (which is way too low), but the manufacturers lobbied for 120Hz, which is twice the AC current frequency. 120Hz LEDs have been known to induce stress, epileptic seizures, eyestrain, migraine, and other problems. The battle to save costs at the expense of customers rages on.