When I re-equip Brutalizer with Jax legend ability (from one unit to the other) do I still get the additional +2 according to the new rules?

Yes, you will receive the additional +2 Might bonus when you use Jax's legend ability to move Brutalizer from one unit to another.

According to the ruling in FAQ #8566 and the card's effect, the +2 Might bonus is granted if the equipment was attached to the unit "this turn." When you use Jax's ability to move Brutalizer to a different unit, the equipment detaches from the first unit and attaches to the second. Because it is now attached to the new unit during the current turn, the condition "If this was attached to me this turn" is met for that new unit.

Sequence of events:

1. Detach: You activate Jax's ability to move Brutalizer. It detaches from the first unit. The first unit immediately loses all bonuses from Brutalizer (the base +1 Might and the +2 Might bonus).
2. Attach: Brutalizer attaches to the new unit.
3. Effect Check: The new unit checks the condition on Brutalizer. Since it was attached to this unit during the current turn, the unit gains the +1 base Might from the equipment and the +2 Might bonus from the effect, for a total of +3 Might.

Important Note: This only works when moving the equipment to a different unit. As clarified in FAQ #8705, under Rule 434.1, attempting to reattach an equipment to the same unit it is already attached to has no effect, so you cannot use this method to "refresh" the bonus on the same unit.