AIM-120 was started as a project to replace painfully ineffective AIM-7 Sparrow and AIM-54 Phoenix (which are only effective against heavy bombers and (in case of later-iteration AIM-54) non-maneuvering fighters). It was to be relatively small BVR missile, so as to be able to be carried by the F-16.
Meteor is a result of joint European project to develop BVR missile to replace BAe Dynamics Skyflash. It was to be capable of shooting down a variety of targets, including low-RCS UAVs and cruise missiles, as well as maneuvering fighters of Flanker family. Another requirement was compatibility with Typhoon’s semi-recessed fuselage hardpoints, originally designed for AIM-120.
AIM-120D is a further evolution of US AIM-120 BVR AAM series. It uses classic fuel+oxygen combustion mix, and does not rely on air flow from outside. In fact, it uses the same engine as AIM-120C, with improvements being mainly in electronics. However, it has been reported that engine malfunctions in cold environments – exactly where it is most likely to be used.
Meteor is a ramjet BVR AAM. As such, it does not carry onboard oxygen, but rather uses oxygen from surrounding air, allowing it to hold more fuel. Result is better acceleration, top speed, and range for a given missile size.
While Meteor may not have as large maximum range as AIM-120D (only figure I have for Meteor is “more than 100 km”, with 100 km being “optimal range”, versus public figure of 160 km for AIM-120D), it is faster, and thus more deadly at any range it can reach. This is important, as BVR missiles are never fired at maximum range due to meager Pk against fighter aircraft. However, range varies on altitude, with best range for both missile types being achieved in high-altitude rare-atmosphere conditions, where maneuverability is almost nonexistent; at sea level, range is not much more than visual. Velocity loss after burn-out also varies with altitude, with 25% of current velocity being lost every 150 s at 24 km, 25 s at 12 km and 5 s at sea level.
Range can be reduced even further if enemy uses jammers. Thus, large NEZ (no-escape zone) is far more important. (To explain terminology here, NEZ is NOT a zone where a hit is guaranteed; rather, it is a zone where enemy aircraft cannot outrun missile, waiting for it to run out of fuel, but rather has to outturn it). Higher speed allows it to reduce time to target, and thus opponent’s reaction time, as well as to retain energy for longer after engine has burned out.
In fact, Meteor’s NEZ was to be three times as large as that of AIM-120B. Active version of missile is equipped with radar Aster, designed to shoot down cruise missiles, which thus can be used against targets with low RCS.
However, both missiles are BVR, making their actual value questionable. In fact, jamming and IFF issues mean that BVR missiles are far more likely to be used as a WVR weapon than in their intended purpose. While AIM-120 did achieve 6 BVR kills out of 13 firings, all but one were against non-maneuvering targets with no ECM and no awareness of missile. By comparing difference in Pk between maneuvering and non-maneuvering targets for AIM-9, it can be concluded that AIM-120 will achieve Pk of at most 11%; however, it is larger and heavier than AIM-9, as well as more vulnerable to countermeasures, so even that is an optimistic estimate.
EDIT: Meteor is estimated to have a range of 250-300 km with ballistic flight path, which suggests an improvement over initially cited goal. That being said, best option is to wait for performance figures after it enters service.