Well, Eidolons are, in general, smaller and more organic than Evangelions, so they have a comparative reach and strength disadvantage, and are more prone to going berserk. Also, they have less versatility. For instance, ABMU-03 and -04 are too lightly built to handle weapons like positron rifles. Oblivion's biggest advantage is it's speed, Prometheus's is it's agility. Heavy weapons would remove those advantages.
ABMU-02, Nemesis, is more versatile, but unless it's in a berserker mode, heavy weapons also slow it down severely. It has a special carriage backpack system to allow it to carry multiple heavy weapons and engage at range, but in order to actually fight effectively at close range, it needs to expend it's ammo and ditch the backpack. It could go berserker (one of the reasons Constance is a good pilot is because she has a fair amount of control when her Eidolon goes berserk), but it would result in the destruction of it's weapons carriage. ABMU-05, Morningstar, only uses it's claws, teeth, wings and AT Field as weapons because anything more would just be an impediment to it's movement. ABMU-06, Perun, has strength approaching that of the Evangelions, but would have to ditch all of it's armor in order to match their speed.
In other words, the Evangelions are much bigger, stronger, and more versatile than the Eidolons on a per unit basis, basically battleships. However, the Eidolons are much cheaper, much less labor and maintenance intensive, and can be built in larger numbers for a variety of roles-Essentially, they are cruisers.
However, even a cruiser can take out a battleship with the right crew, right weapons and right tactics. And a Berserking or a Rogue Eidolon is just as dangerous as an Evangelion.