I do not own either of these weapons, but I do know that the Minigun is overall less good than the Chain gun. Although the mag capacity and damage may seem sweet, there are a select few flaws with the Minigun which are over-powered by the Chain gun.
Some of these flaws are the spin-up time, reload time, recoil, mech turning speed, optimal/max range, a shot delay, no double-damage chance, and wide hit-cone.
The Chain gun does have a spin-up time, but the spin-up time is different with the gun shooting slowly and gradually firing more rapidly the more you shoot. The Minigun, however, must spin its barrel to gain momentum before shooting which is an obvious big red flag. This can be prevented with the use of implants, but I believe this would be a waste of your pilot implant slots.
The Chain gun also has a much faster reload time, no mech swivel speed decrease, a double-damage chance, a longer optimal/max range, no shot delay, no recoil, and a hit-cone of 1.2 whereas the Minigun has a hit-cone of 2.4. Still, the Minigun does a significantly larger amount of damage, but if I were you I would get the Chain gun.