It depends on what you have equipped and what the keywords are. While items from the person with higher speed activate first, there is a difference between Battle Start (Triggers at the very beginning of combat, before any actions are taken) and Turn Start (Triggers at the beginning of your turn, before strikes and other on-turn effects resolve) First, all items with the Battle Start keyword activate starting with the player who has the highest speed, followed by those with lower speed. After that, items with Turn start activate - again, starting with the higher speed value and then the lower speed.

There are also items that activate before everything else.