It is correct that in more recent PD radars look down range is no longer terribly different from look up range (APG-66 is hardly a representative radar any more these days, and the overlapping ranges for l/d and l/u performance respectively render those figures rather useless for comparison). Doppler filtering works extremely well nowadays.
So what that Chinese source implicitly tells us is that the J-16 radar effectively is slightly longer ranged (maybe 10 - 15%) than the Irbis in the Su-35 - fair enough. They both have about the same antenna diameter, they're both X-band (meaning the number of radiating elements and hence antenna gain will be very close) and, as the Bars/Irbis family of PESAs uniquely have an AESA-like distributed receive signal path, very similar receiver sensitivity. Assuming the J-16 AESA has a fairly typical per-element transmit power of around 10W and a TRM count of some 2000 modules (X-band, 0.9m diameter array) we get a transmitter power in the same 20kW ball park as the Irbis' centralized two-stage TWT (which however implies wave guide losses that don't accrue in an AESA). Makes sense, the available cooling and generator capacity (if that's the long pole in the tent) should also match closely, given the related airframe platforms.
Antenna gain similar, transmitter power similar (with an advantage for the AESA, due to not suffering wave guide losses), receiver sensitivity similar - radar range equation says they'll be close, lo & behold, they are. I don't see why this is such a big deal - there's nothing very much surprising about it, just basic physics.
PESA will surely have less receiving and transmit gain. There is going to be signal losses between the travel path of the main amp to the emitters in the elements. This includes the line feeds and duplexers in the sub array level, and then between the phase shifters themselves. That's for the transmit part. On the receive part, there is going to be signal losses between the receiving element to the A/D converters, as there is more path between the receiver to the A/D converter which is located way more downstream on the PESA, perhaps at the subarray level.
On the AESA, the amp is on the module and the travel distance between amp and the emitter is very short. If the AESA is using TTD phase shifting instead of electro-magnetic ones, even less losses. On the AESA, the A/D converter is on the module itself, so the receiver to A/D converter path is also very short.
The use of electrical or magnetic phase shifters means these shifters need a reset time between transmit and receive. This is called dead time so during the phase of the pulse time, the element is neither transmitting or receiving. This results in shorter duty times and receive times compared to an AESA.
IRBIS or BARS main AMP must be strong enough to overcome these disadvantages to justify a PESA over an AESA. Older radars can still try to outpower an AESA by having a much more powerful main amp (TWT, Klystron, Magnetron, etc,.)
The main advantage of AESA over PESA and older radars is sheer agility, although modern amps for PESA and mechanical radars have shown to be agile too. The purpose of this agility is not much as for range and power, but ESM/ECM resistance. ESM resistance as not being able for the enemy to detect your emissions through LPI, and ECM resistance means its much more difficult to spoof and jam.
Having increased range in your radar only means that you are the one being detected earlier by your opponent through passive ESM.
