The difference is the way your wrists and arms are positioned when you use the EZ bar vs a straight bar.
Do this. Put your right palm facing down to the floor, have your right arm positioned in the same way as you would when in bicep curl position. Now put your left fingers on your right bicep and turn your palm up until its straight up.
When your palm is fully straight up you'll notice that your bicep is the most tensed. So it might be that a persons arms use additional muscles when their arms aren't exactly straight up.
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