First, I am answering with the understanding that you are asking about aircraft losses, and not AA gun losses. AA guns should always be chosen by the defender.
The league rule is that you follow the rule book.
The rule book says that the attacker always gets to choose aircraft casualties. This includes SBR. Wheatbeer seems to be a bit confused, so I will attempt to help with that.
If you SBR a base with tacs and strat bombers, and you take AA hit(s), you may choose your casualties (probably tacs).
However, when you SBR multiple facilities at once, you are first dividing your aircraft into groups. The reason the attacker sometimes has to take off strategic bombers and not tactical bombers is because the tactical bombers are attacking a different facility than the strategic bombers.
Example:
Strat bomb UK with 2 tactical and 4 strategic bombers.
Air battle is complete, no losses for Axis.
Axis player allocates 1 tactical and 1 strategic bomber to the air base
Axis player allocates 1 tactical bomber to the naval base
Axis player allocates 3 strategic bombers to the IC
You are to roll AA separately for each of the facilities.
2 AA shots for the air base
1 AA shot for the naval base
3 AA shots for the IC
If the air base AA hits, the Axis player chooses a casualty - could be tac or strat
If the naval base hits, the tactical bomber attacking the naval base is shot down
If the IC hits, the Axis player must lose strat bomber(s)
Triple A fouls this all up completely. See my list of rules that Triple A does not properly follow here: https://docs.google.com/document/d/1cS3hFwoBP0rWr3208jw1LAtCvHYa9Ji9uU8PwbCMIwM/edit
Item #4 is SBR
Note also that Triple A (Item 4b) prompts you to choose facility targets before the air battle, and this is also incorrect.