A US LLC is usually the better fit as an operating company. Formation is fast and cheap. Upkeep is easier too, and the company works much better with Stripe, PayPal, US banks, and contracts with Western clients.
A Panama S.A. is better for other things. Use it when you want a non-US company for holding assets, international invoicing, pairing with a Panama foundation or residency, or you generally need a structure outside the US legal and tax system. Privacy alone is not the reason. Many US states, such as Wyoming or New Mexico, already handle that well.
If the company mainly needs to get paid and look normal to payment processors, start with the LLC. If it needs to hold assets, sit outside the US, or connect to other structures in Panama, use the S.A. A lot of clients use both.