I did around 40 minutes of testing with two friends. Here are the main differences:
The Sidewinder will hit in 85% in a duel (without enemy using CM). The 15% being some dead angles, weird directions your target is flying and distances that are too close.
In a team fight the Sidewinder will hit in most cases where CM's / CD's are not being used. The speed of the missile also lets you cover up the sound much more easy with a CD.
The Firestalker in a duel will hit only in 65% of the times if you opponent knows what he is doing. Even when the target is running from you, it is easy to dodge. In the pressure of a
team fight it also only goes up to 80%. However, it is much more easy to use as a spamming missile. The ammo count and short refire time supports that. Together with others using
CD's on the same target, more than often the target of a team fight can be easily baited to use all his CM's within a short time. Once that happens you the DPS is pretty decent.
But even here if the targets does manually uses CM's, that can be avoided.
Nonetheless, I agree that taking a closer look at missiles and the diversity might be a good idea.