Activation phase: Activate ship first.
Pilot skill costs points. You pay points for choosing your action when you know what the enemy already did. In most cases you want to activate your ships last. The only exception to this is if your strategy involves blocking to force overlapping. For lists with mainly PS1 and perhaps PS2 initiative is an advantage. More often than not it is a disadvantage.
disadvantage
There's a slight advantage there, and also of course, when you actively try to block.
When both your own ships and those of your opponent are almost in "furball" range, getting your own actions and denying his is huge. This is not a forced overlap per se but more a result of having many ships (e.g. 4 vs 7) in play.
I see the above happen in every game and it makes me long for true 3D, especially when I don't have the initiative.