Deloitte GPS internship or PwC Cloud and Digital internship

Hi everyone, 

 I go to a non target school and did a summer internship at PwC. Was given a return offer in tech consulting (think erp systems). I accepted the return offer for the summer 2024 internship. I am not interested in being siloed into a certain system and I am far more interested in management and strategy consulting. So far the only other offer that is favorable is Deloitte GPS summer scholar. The issue is I already accepted PwC and the PwC offer is more favorable in terms of pay and location. Deloitte did offer me the choice to look to choose my project based on their offering portfolio. If I want to do management consulting or strategy consulting fulltime would it really matter which offer I decide on? I know internal movement is rare and opportunities to move are sparse. Thanks in advance for any insight!