you guys are forgetting, this game does a poor portrayal of the Eclipse's power, it's huge shield, and it's mass of armor. plus, it had more firepower then the Executor in all ways. while the Eclipse has less guns the Executor, true, it would keep those guns operational longer because of the super strong shields. there is no way an Executor could beat eclipse 1v1, eclipse is by far superior.
now, that said, most of the time massive fleets are based around them, and they fight as well. so, depending on fleet size and Compostion, plus tactics, an Executor fleet could beat a Eclipse fleet, but not in a 1v1 battle
{edit: though that i've done more research, i want to show this, which recently put on the Moddb page for the Vader's New Order: Empire Surrounded mod. this is what i put}:
Eclipse and Executor serve different purposes. while the 19 km Executor is supposed to be a fleet flagship/centerpiece, the Eclipse was supposed to be the final culmination of the Tarkin doctrine.
Executor is the most mass-produced SSD in galactic histroy. with at least 15 built, with more rumored to exist, they were 19km long and 4km across. the vessels were armed with 2,000 turbolasers, 2,000 heavy turbolasers, 500 ion cannons, and 500 concussion missile launchers, plus 40 tractor beams. they normal held 2 wings of Tie fighters, but could hold up to 20 wings of fighters. the also carried 5 legions of stormtroopers, 38,000 ground troops. to support those, they had 30 AT-ATs, 40 AT-STs, 5 pre fabricated bases, and all the ships to take them down to the ground. not counting stormtroopers, the Executor normally had a crew of 280,000 + men. the ship held enough consumables for 4 years
there were multiple variations of this SSD class. notable ones were Knight Hammer, Terror, and others. this was the most widely used SSD as well, as notable users were the Imperial Remnant, Zsinj's empire, the Pentastar Alignment, the Eriadu Authority, Warlord Drommel, the Duskhan League, and even the New Republic. the last executor, Guardian, was the only one to survive the Yuuzhan Vong war, though it's fate afterwards is unknown.
the Eclipse was the ultimate Terror weapon ever made. 17.5km long, it had 1 weapon that made it truly fearsome, nevermind anything else: an Axial superlaser capable of cracking planets crusts and targeting and destroying even SSDs in 1 blast. it's armor was so thick and strong that the Eclipse could just ram opponents and destroy them. it also came equipped with 4 gravity well generators. armed with 550 heavy laser cannons, 500 turbolasers, 75 ion cannons, and 100 tractor beams, it relied more on the superlaser/shields/armor to destroy fleets. normal aircraft composition was 50 squadrons of Tie interceptors, and 8 squadrons of bombers. it also held 100 AT-AT walkers, and 5 pre-fabricated bases. it also held 150,000 stormtroopers. it's crew, not including troops, was 704,000+.
only 2 were ever made. 1 was destroyed in one of Palpatine's own force storms. the other one was destroyed after Palpatine's final death. hijacked by R2-D2, it was rammed headlong into the galaxy gun, which resulted in the destruction of Eclipse II, the galaxy gun, Byss, and the entire Byss defense fleet.
palpatine also made 4 Sovereign class SSDs, with more planned. these were the production variants of eclipse, with less armament, armor, shields, and a weaker superlaser. all 4 were destroyed by the Destruction of Byss.
in a fight, if the Executor was in front of the eclipse, the eclipse would win. but, if the executor was alongside or behind the eclipse, the the likely result would be the Eclipse's eventually destruction. while video games aren't always the best at portraying it, the eclipse's superlaser could only fire about twenty degrees away from where the bow of the ship was pointing. so, if the Executor captain was smart and got his ship alongside the eclipse, the likely result would be the destruction of Palpatine's pride and joy