Y could totally beat the pants off of X. Of course, neither of them are a match for Z, but what is?
Round 1: Master Chief [halo] vs Samus [metroid] (bonus video)
Arena: apocalyptic city ruins.
Power ups: Ominous-Mode, aka all power ups are available. In the case of MC they take the form of radioed cache drops.
I'm only passingly familiar with Halo, and it's been a while since I played any Metroid, so my information and analysis may be incomplete. Also, I'm not counting completely one-sided powerups like invincibility (either the Halo and multiplayer Metroid Prime 2 powerup, or the total invulnerability of Phazon mode) or bugged out stuff like the Murder Beam (everything dies, possibly even the game) or the Space-Time Beam (resets space and time, or maybe stops them forever, depending on which direction you're facing), because then any comparison is kinda meaningless.
Master Chief vs. Samus, basics are exactly what Oslecamo said. Samus is working off of a much higher tech base which can equal or exceed most everything that MC has access to. The only things I know of that MC has access to on an infantry scale that Samus can't replicate is the one-hit KO-ish beam sword thing, cloaking, and regenerating shields. Cloaking may provide a first strike to MC if Samus is unaware of the possibility of an engagement entirely and doesn't even think to scan, but afterwards her superior detection systems (infrared, x-ray, sonar, and trans-dimensional scanning) should pretty well negate it if they're going head-to-head. The beam sword is nasty, but then so are power bombs and the hyper beam, and freeze + missile has always been a two-hit KO anyways. MC's regenerating shields are his only significant advantage, allowing him to win a battle of attrition if he can secure sufficient ammunition from his supply drops. Samus's energy shields don't inherently regenerate, so if MC can get in enough pot shots without taking sufficient return fire to hurt the armor beneath his shields while keeping Samus out of range for her Grapple Beam (which has an upgrade to let it drain energy back in Metroid Prime 3), he could theoretically wear her down and claim a victory. He won't, of course, because Samus's extreme mobility (high speed and self-powered flight, mostly), will ensure that she can control the engagements, being able to easily escape or pursue, so attrition is a completely non-viable option.
Beyond the infantry scale, some of the various Halo fighter ships should be a match for Samus's gunship. The gunship is probably capable of some ship-to-ship combat, but it's really optimized as a transport/bomber (at least from what we see in-game), so a decent air superiority fighter should be able to take it down. That said, Samus's power armor is plenty capable of ground-to-air combat, so she could well serve as an effective anti-fighter deterrent if she just lacks herself onto her gunship's outer hull and shoots from there while it's on auto-pilot. Case in point, she consistently takes on and crushes Ridley, who is basically an air superiority dragon. There's not really enough information to push it strongly one way or another, although I'd give the edge to Halo's fighter craft even over Samus's gunship with Samus firing back.
At a military scale, Master Chief is part of the UNSC military, while Samus is only a contractor for the Galactic Federation. Master Chief just has more forces that he can reliably call on for reinforcements, being part of (and not at the bottom of) a large chain of command. Samus can only really count on herself, and I don't get the impression that she has the clout to independently call in assistance from the GF navy. If the actual militaries involved were to clash, there's just not enough information to make any meaningful comparisons.
In terms of being able to deal with ground missions, against targets other than each other, Samus wins, no contest. MC's cloaking potentially allows for more effective stealth than Samus's mobility systems and morph ball, but its short duration is a killer. Samus herself is no slouch at infiltration even without her power suit's advanced technology, though. With it, she can access virtually any location, terrain be damned. Self-propelled flight is just so useful. Solid walls are a problem for anyone not from Red Faction, but for anything less than video game unbreakable, Samus is much better at making walls into suggestions. Samus's power suit's scanning and electronic warfare suites will make Cortana drool. In terms of combat effectiveness, see above regarding head-to-head at the infantry scale. Both MC and Samus are proven against conventional and unconventional military forces, but Samus has way more experience fighting off and blowing up weird monsters, gigantic robots, and frickin' space dragons than MC would even believe. Also, I'm pretty sure Samus has blown up more planets than Master Chief has, and she's definitely destabilized more parallel universes.