You can read Epic's court filing but the tl;dr is that Epic alleges that the terms of the contract restrict Epic and other parties from competing with Apple, that Apple uses their market power in one area to get an unfair advantage in other areas (such as payment processing), and they cite the Sherman act as the primary legal basis of their claim that those terms are illegal.

This case is likely to last for years so it is very much too soon to be predicting who will win.