Heavy Weapons are quite good in Call of Duty Advanced Warfare. The maps are generally open and have a lot of medium and long range combat. Some of the heavy weapons are interesting, such as the XMG which is always duel wielded, but are generally too specialized to be considered the best Heavy Weapon. Hence the contest is between the Pytaek, EM1 and Ameli. I believe the Ameli is the best Heavy Weapon in Call of Duty Advanced Warfare.

Ameli Best Class Setup
Best Primary Weapon in Advanced Warfare
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The Ameli is the Best Heavy Weapon in Advanced Warfare

I like the EM1, which is essentially a laser rifle that shoots a continuous beam. However, it has a very slow fire rate which translates to not very much damage being done. I often started shooting first and still died to some Submachine guns. Also, the beam points out exactly where you are so any enemy that sees the beam will know how to find you.

The Pytaek is also reasonably good, but I feel that it is an inferior version of the Ameli. It has very low handling and mobility but does have much more accuracy. But the Ameli has significantly more range and a higher fire rate making it much more deadly at medium and long range. Hence I believe that the Ameli is the best Heavy Weapon in Call of Duty Advanced Warfare.