Playing the core campaign and came across a situation where a rebel player fired at an imperial elite leader who has 1 black and 1 white defence dice.

Overcharger states 'Deplete this card when you declare an attack, Remove 1 die from the targets defence pool.'

If there is only a single dice its not an issue, but when there are two, who chooses?

Compared to the Diala Passil ability which says 'when you declare a 'sabre' attack. Choose and remove one dice from targets defence pool.

The key word missing from overcharger is Choose. So does the defender select the dice or the attacker?

In X-Wing the general rule is do what the card says and don't do what the card doesn't say. With the difference in wording, I'm thinking the defender would choose but not 100% sure.

@digivamp I'd say that your rule of thumb is still a good one, with this addendum for IA:

"If there's a decision to be made, the player who played the card gets to choose" (unless its explicitly stated otherwise on the card). In this case the attacker would choose the die to remove, since he/she is the one using the ability.

Another example of this would be the "push" keyword. If you use an ability that says "push" then you control where the figure goes, no matter who owns the figure. If it's a mission rule (such as a massive figure standing on you, forcing you to be pushed) then the rules specifically call out that it is the person who owns the figure that decides.

The figure (player) with the ability decides unless explicitly specified otherwise.