@gambit plz compare both missiles on their published parameters, it is important to conclude discussion here.
For intellectual honesty's sake -- I cannot.
I was in that business -- in and out of the military -- long enough to know better. Look up on how we estimated and valued the MIG-25. For US, it was a Soviet 'wonder weapon' that could render the USAF next to helpless. Then we finally had the Foxbat in our hands to study and what a piece of junk it was.
Take missile navigation laws, for example...
IEEE Xplore Abstract
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Two robust homing missile guidance laws based on sliding mode control theory
Two new guidance laws for short range homing missiles are developed by invoking the sliding mode control (SMC) theory. Guidance law 1 as structured around the basic proportional navigation (PN), with an additive switching term, which is a function of the line of sight (LOS) rate alone. An adaptive procedure is suggested to select the gain of the switching term, in order to reduce chattering. This guidance law is nearly as simple to implement as the PN itself and does not require any explicit target maneuver estimation. Guidance law 2, based on a first order sliding surface, is designed such that it results in a continuous acceleration law, thereby reducing the chattering problem. While explicitly taking into account the effect of aerodynamic drag, it requires the second derivatives of LOS angle and range, which are not directly measured. An estimation scheme, again based on sliding mode theory, is presented to estimate these quantities.
Do we know the details of these laws for either missile ?
Base on that brief abstract, I have an idea of what the authors were talking about, but it is pointless because we do not know the pro-nav derivatives that both the AMRAAM and the MICA use. I know enough to be confident that in a tail chase situation, both missiles will resort to pure pursuit laws...
Pursuit guidance - Wikipedia, the free encyclopedia
...But I do not know the details about angular differences that missiles' radars will detect when the target begins to maneuver so that each missile will begin to deviate from pure pursuit guidance and into pro-nav based complex algorithms.
Proportional Navigation is the foundation of both missile guidance and ship collision avoidance.
Cambridge Journals Online - The Journal of Navigation - Abstract - A Line of Sight Counteraction Navigation Algorithm for Ship Encounter Collision Avoidance
A new navigation method, called a Line of Sight Counteraction Navigation (LOSCAN) algorithm has been introduced to aid manoeuvre decision making for collision avoidance based on a two-ship encounter. The LOSCAN algorithm is derived from an extension of the basic principle of traditional missile proportional navigation, recognising that the objective of the latter is target capture rather than target avoidance.
Based upon the above abstract, I can say that the initial algorithm for LOSCAN is exactly as missile guidance -- to capture the target, but then the capture solution is routed to an exclusion filter to produce real time continuous updates to the ship's pilot on what is the best and safest path to avoid the other ship. The entire set up depends absolutely on radar resolutions of all targets within the scan field. In a multiple targets situation, each target is treated through the LOSCAN algorithm as if it is still one ship vs one ship situation.
We can have better guesses on ship avoidance laws than on how missiles go after jet fighters.
Raytheon and MBDA can make all the public announcements about their missiles but until both missiles meet their targets in actual combat, there is no way to intellectually honestly say which is fighter/missile the better combination. With the AMRAAM, at least we have Iraq and Serbia to give us an idea of how the AMRAAM performed in real world situations. We do not have any combat experience for the MICA.
According to Raytheon, in a tail chase situation, best range estimation for the AMRAAM is roughly 20 km, but in a head on scenario, best range increases to 70 km. Does that mean the AMRAAM user should go for the head-on shot every time ? Hardly. No pilot like head-on engagement. But precisely because how pro-nav laws works, the head-on engagement offers the highest kill probability. In a head-on engagement, radar targets produced by countermeasures will trail the fighter that dispensed them by at least an order of magnitude, rendering radar countermeasures at least 50% ineffective, and that ineffectiveness factor increases as the enemy fighter approaches the AMRAAM user. The bad part is that the head-on engagement put the AMRAAM user into the same vulnerability as the fighter he is trying to kill. So why should he put himself at such risk ? Better off to try to get into a tail chase engagement but with shorter distance.
What about SLAVE or BORE coupling ? In SLAVE mode, the missile, AMRAAM or MICA, is guided by the parent radar as to what target to go after. In BORE, both parent and missile looks straight ahead for any target that happens to be within the boresight aperture. SLAVE is good in multiple targets situations as the pilot can assign each of his missiles to specific radar targets. BORE is good in close quarter combat where a wingman offers enough protection to allow lead to focus on a single target. The issue here is that the decision to SLAVE or BORE the missile depends on the pilot and his judgement at the immediate combat situation. If he chose wrong and the missile failed, how is that a negative point against the missile ? Assume that the AMRAAM is somehow inferior to the MICA. If the AMRAAM user/pilot was good enough to isolate his target into a situation where BORE is best and the missile shot was a kill, how is that a positive for the AMRAAM ? In SLAVE mode, the better the parent radar, the better the odds that the pilot can position his target into the missile's claimed 'no escape zone', therefore, the better odds for a kill. The AMRAAM and the MICA are BVR weapons but make no mistake about it, if the pilot deems the situation is better served with the BVR missile even when he is within visual range, he will use the BVR weapon.
I know that people want absolute answers but that is not going to happen. There are too many variables and most important of all -- it is the pilot.