This is an excellent question. I too am struggling with the use of the machine gun. I deploy one in every mission, but find the weapon's wielder has a harder time scoring kills than his comrades armed with submachine guns. The sniper, of course, is the queen of the battlefield, and is so very wonderful at the long-range firefight. The grenade launcher, despite its short range, is a fantastic clearing weapon.
My understanding is that a machine gun will be slightly less accurate than an assault rifle, and rather less accurate than an M-16-style weapon. However, it has the ability to sustain more automatic fire, and can therefore bring a lot of rounds down on target, especially groups of enemies. In the past, I've deployed the machine gunner to hold choke-points along the main axis of attack, but I've found that he has more trouble holding such a position than an agent armed with a submachine gun.
Perhaps the range and accuracy of the machine gun needs to be tweaked to be a little bit better, and the full-auto fire setting should be increased to some 30 rounds, to really get the full effect of a machine gun to happen. A machine gun must be able to significantly outperform smaller weapons in automatic fire, although it's true that even a proper machine gun is best fired in short bursts, so as not to overheat the barrel. However, doing so might keep the machine gun relevant.
While I'm on the topic, I think something needs to be checked on the assault rifle as well. I find that assault-rifle wielders rarely tend to get off more than a single shot at a time in reaction fire, even when set to 3-round burst or full auto. As a result, assault rifle agents are weak and unreliable in reaction fire compared to all their comrades, which is a shame, because I like to have a balanced and diverse squad. Really, an assault rifle should be the standard weapon for the larger maps, while the submachine gun should be intended more for FIBUA (inside buildings). I'd like to deploy the following squad:
1 sniper (a wonderful weapon, especially when your sniper gets good)
1 grenade launcher agent with a sidearm (These days I never leave the base without one. Why storm, when you can blast them out?)
1 machine gunner (needs higher rate of fire to hold choke points like a machine gun could)
2 assault rifles (needs more reliable multi-shot reaction fire)
2 submachine guns
1 medic armed with a submachine gun (pretty standard military practice)
I'd like to use the shotgun and flamethrower more, but they're too special and limited, I find, for the various battles. Maybe that's why a lot of special forces and SWAT police don't carry them. Still, I'd love to use them; there's just not enough room, not enough agents. But then again, everyone has his/her own
style, which is why this game is so, so great. I see various schools of thought emerging, various kinds of practice emerging, different teams doing things different ways, but getting the job done. Love the game, people.