Shield mitigation increases as a ship is attacked, and represents the shield adjusting itself to the enemy's weapon. If you check one of your ships as it is taking damage (red circle around it), you will notice that its shield mitigation increases. You probably just compared ships that didn't receive incoming fire with ships that got a lot.

Advent ships receive a bonus to base and maximum shield mitigation when fighting in their own culture.

Frigate shield mitigation maxes out at 57% (again, Advent frigates can have up to 67% mitigation).

Capital ship mitigation depends on level. Maximum mitigation is 65% for a level 1 cap and increases by 1.111% per level (so a level 10 capital can have 75% mitigation - once again, Advent caps can have up to 85% mitigation).

I do remember the rates of mitigation increase and decrease were posted somewhere else, though I don't know if this corresponds:

1.25% increase per damage taken, 1% decrease per second

That may be why your losing close battles. Carriers and transports are usually at the bottom of my list. I prefer to target enemy cap ships or cruisers first. The best way to counter fighters and bombers in my opinion is with flak frigates. I find if I chase transports around the map I end up stringing my fleet out and getting picked apart.

I am by no means an expert so if I am incorrect then someone please correct me.