The land based L-band NNIIRT Protivnik GE with 8.5 x 5.5 m array , has a 500 KW of peak power .
As per Rosoboronexport , it has a detection range 240 km of a target that is 1.5 sq.m of RCS at height 5km .
And as per NPP pulsar the L-band wing based radar on Su-35 has a nominal power of 200 WT (200*12= 2.4 kw per array and 4.8 kw for both arrays ) .
The Protivnik radar will scan a huge portion of the sky with its big antenna. The radar on su-35 will scan a much smaller area.
Power is linked to how you concentrate your beam.
With a 2 kW radar concentrated into a small cone of detection like on most x radar in the fighter's noses you can spot a target much better than if you use a 500kW scanning for half of the sky at once...
The difference between a stealth plane scanning for a conventional one with its onboard X band radar would operate in a conventional way: it scan a large area first once it get some result perform a narrow scan one and begin to track it , all of this transitioning smoothly from one phase to the successive until it get all the data it need to engage it.
I expect instead that in the opposite case they would need a consistent amount of time and a less linear shifting from alet's say the first wide area scan made with the L-band radar to the fine tracking necessary to effectively engage the stealth opponent.
So, one plane would made it in a single stage, the second would perform a series of successive searches receiving just a part of the necessary data from each of them.
So the L -band in wide search mode would detect the stealth plan at fair distance but would get just a general idea of where is it, so it would need to made a second one in a narrow mode to refine such location and begin a preliminary tracking, after it would pass it to the nose band radar in the x -band that would have to perform a second search in the delimited space in which the former radar has recognized the presence of a stealth plane and keep on narrowing it until it get an enough precise location and finally going to the fine tracking necessary to engage it.
So, in the end it would need more time to get to the same (or better said a comparable, as I still expect it would need to use a greater portion of its own search power to engage simultaneously a smaller number of targets at the same time) result but it would get it anyway.
So the presence of two radars is IMHO
absolutely necessary: the L band one assure the capacity of wide area search and an early detection range even superior to the one of the stealth plane own radar, the X band one the fine tracking capabilities necessary to effectively engage it.
Still, I think that the Stealth one would reach the condition necessary to launch its own missiles before of the other.
BUT not the necessary distance to do it with an effective chance to hit anything.