If I'm attacking two tanks at a battlefield, does the tank with the highest might become the first target, or can the attacker choose between the two?

If you are attacking two units with the Tank keyword at the same battlefield, the attacker can choose between them when assigning combat damage.

According to Rule 815.1.c.2:

"If more than one unit with Tank is present with the same controller in Combat, damage may be assigned to any of them. Units without Tank are invalid assignments until all units with Tank have lethal damage assigned to them."

Additionally, Rule 460.2.c.6 clarifies how to handle multiple units with the same priority requirements:

"If multiple Units have abilities or effects that require a player to assign them damage with the same priority, that player may assign damage to those units in any order."

Summary of the Damage Assignment Process:

1. Tank Priority: Because both units have the Tank keyword, they share the highest priority for being assigned combat damage.
2. Attacker's Choice: You (the attacker) may choose which of the two Tanks to assign lethal damage to first.
3. Completion: Once you have assigned lethal damage to your first choice, you must then assign any remaining damage to the second Tank before you are permitted to assign damage to any other units at that battlefield that do not have the Tank keyword.

The Might of the units does not change the priority order of the Tank keyword; it only dictates how much damage is required to make the assigned damage "lethal."