In a vacuum. The aerodynamics aren't possibly the same.

Surely the aerodynamics are better for firing a missile backwards.

If you fire it forwards, the missile has to accelerate through whatever air resistance you're both already experiencing through even more air resistance to get to the target. That's hard.

If you fire backwards, the missile uses air resistance to accelerate towards (i.e. slow down) towards the target. Even when it goes through 0mph relative to the air and continues to accelerate, the resistance will be much less as it approaches an even higher closing velocity in a shorter period of time.

Modern fighters are all about sensing and targeting the enemy first since missiles are so deadly. The missiles are much faster than the planes so which way the missile is pointed at matters less and most of the time it is better to be pointed forward.

So the optimizations and tradeoffs are in sensing and targeting further away or being able to rotate a sensor to target an enemy off bore.

If you fire it backwards, when it first launches it will be traveling backwards relative to the airflow. So you would have to make a missile that can fly forwards or backwards. Probably not impossible but it must add some difficulty.

hmm, yeah that sounds challenging, but spacex does it when landing the first stage :)

I would guess that the speed at which air moves over the missile's control surfaces has a large effect on its ability to steer to meet the target.

But, missiles can't maneuver at 0mph airspeed even if traveling at 600mph in the frame of reference of a plane.