Sovereign-class Explorer
Length: 685 meters
Width: 224 meters
Height: 88 meters
Weight: 3,225,000 metric tons
Capacity: 58,299 metric tons
Weapons:
12 Type XII Phaser arrays capable of firing 5 beams each at full power (16 MW), effective range 300,000 km
5 Rapid-Fire Photon\Quantum Torpedo Launchers, capable of 10 Torpedoes in 50 seconds, 1 minute reload. effective range 4,050,000 km.
Payload:
325 Photon Torpedoes at 63.4 megatons
175 Quantum Torpedoes at 129 megatons
Defense:
26 generators providing 460 MW each covering the vessel
10 cm Ablative Armor capable of withstanding 63.4 megatons directly.
Maximum Sublight: .75c, or 224,844 kilometers per second
Maximum Warp: 9.7 for 12 hours, or 2373C, or 7,114,075,028 km\s (6.5 lightyears\day)
Halcyon-Class UNSC Cruiser
Length: 1170 meters
Width: 352 meters
Height: 414 meters
Weight: ?
Capacity: ?
Weapons:
1 MAC (30,000 km\s launch speed, effective range 100,000 km or less)
300 Archer Missile Pods (? effective range)
40 MLA Autocannons (? effective range)
Payload:
26 Archer missiles per pod, 7800 in total (? yield)
4 SHIVA Nuclear Warheads (? yield)
? MAC rounds (600 ton Ferric-Tungsten)
? MLA Autocannon rounds
Defense:
5 meters Titanium-A Battle Plate (Estimate)
Maximum Sublight: ?
Maximum Slipspace: 2.1 light-years\day (Warp 7.229) 2,191,482,868 km\s
I can't find any better specs for the Halcyon cruiser, and some things are calculated or extrapolated from information on Halopedia. As it stands, with a lack of data about the Halcyon Cruiser, the result is inconclusive.
Speculatively, I would say that Star Trek would win, just because of the higher technology.
In ship-to-ship, Star Trek would utterly destroy Halo vessels, but on the ground, it would be the UNSC and Covenant troops all the way.
Speculatively, of course.