You see the issue here is, neither TFX nor f35 can uses its radar as freely as you think against each other in head to head mode!
because there is a good chance opponent's EW suite will pick you up!
That is the very reason why world's first stealth aircraft F117 didn't have any radar in the first place.
But with the introduction of f22 Raptor, a new generation of radar technology was put into its nose cone of the aircraft.
AESA was very decisive when it first came, because no contemporary RWR or EW system could pick it up at that time because of its very low probability of interception characteristic.
for example, APG-77 can change its frequency bandwidth thousand time per second.
However, one decade later with introduction of f35, we got highly evolved PROCCESING POWER and true SENSOR FUSION technology.
which again, somewhat changes the game in favor of the 'LISTENER' (passive detection) over 'SEEKER' (active detection)
because now, not just today's 5th gen EW systems are far more sensitive than the previous generation, but also, unlike past, now with the sensor fusion capability it got directly integrated with main SUPER computer of the aircraft!
Thus, giving it enormous and unprecedented capability.
And that is why in a test in2009, f35 superior EW system was able to pick up Raptor's APG-77s transmission even though it has very good LPI characteristic as i mentioned before.
web.archive.org
With that being the case, in todays air domain stealth fighters primary sensor is its highly sophisticated and super sensitive ELECTRONIC WARFARE suite and electro optical suite, not its FCR even if it is LPI AESA!
for example, that is how BAE system describe AN/ALR-94s capability and implication.
Quote-
"BAE Systems’ AN/ALR-94 digital electronic warfare system geolocates potential threats by detecting adversary radars at significant ranges, ALLOWING THE F-22 RAPTOR TO LIMIT ITS OWN RADAR EMISSIONS, ENABLING IT TO BETTER CONCEAL ITS LOCATION WHEN OPERATING IN HOSTILE TERRITORY"
Unquote-
The AN/ALR-94 protects the F-22 with advanced electronic warfare technology.
www.baesystems.com
Today, against a possible near-peer adversary f35/f22 will use its APG-77/APG-81 in highly selective and limited manner and PRIMARILY rely on its passive detection and sensor fusion capability.
And that is also one of the core reason why the MUM T concept becoming with 5th gen and 6th gen platform becoming more and more critical, as an somewhat expandable drone or wingman carrying sensors on board can ACTIVELY SEARCH for enemy contact while the main expensive manned aircraft like f35 or TFX can remain passive and undetected while listening for the hostile radio transmission.
CONCLUSION-
So in my opinion, sensitivity of the TFX's EW system, EOTS and DASS, plus the degree of it SENSOR FUSION ability would be more decisive against a near-peer adversary than its AESA radar's active detection effort.