Well without knowing the exact numbers (never checked for em) as my hw RM modding experience was limited to sound editing.
I can only quote you what I read in the official patch notes and of statements made by bitvenom, or what I experienced first hand ingame:
The idea for the different stances was that each stance made units behave differently.
For instance: Aggressive stances would reduce their speed but enhance their damage while lowering their defensive powers. Squadrons would stick to their formations no matter what (bug 666 ruined that ofc.) Imagine it as in Freespace2 where you could adjust your fighters settings. Either get speed but be lesser shields and weapon power. And vice versa. Aggressive works best when you’re facing a inferior force and want to destroy them as quickly as possible.
Neutral stances: Units would be well adjusted to a 50% boost on anything. Power levels would be adjusted to have everything equally set… Lesser speed, lesser shields, lesser weapon power… But still the best setting to use if you’re outnumbered or superior in force and want your units to survive as long as possible.
Evasive stances: Are most commonly used when you determine that your forces are losing a fight and you want to get them out of harms way as quickly as possible. It also enhances the chances that they evade weapons fire or outrun their opponents which are in a different stance other than evasive.
In that stance they also break their formation frequently and engage 1on1 what ever you assign them to. It gives units a general speed buff.
Scripting wise for mission design it does make sense to use that stance to simulate some sort of squadron panic (for fighters) as they will break their formations.
As for bug 666: That fix which was recently released is remarkable. Before the fix I never really noticed a difference as to the vanilla classic games… But with it I had seen the difference. Fights felt entirely different. Even the AI forces felt different. It is an unofficial patch well deserved. @bitvenom I just hope that he might someday get us that official patch update fixing that and other aspects of the game. Even an incomplete patch might be an improvement to this game at this point. And as opt. patch surely no harm can get done.