What documents can I present on both sides of the border?

Visa and duty payment

ID, Passport and I believe, border crossing papers/passcard

From MX to USA, visa US passport. From USA to MX, Mexican passport or American passport

Passport, visa if applicable, fill out E19 and payment of rights

Here you have all the details: https://www.crossborderxpress.com/en/requirements

Only cbx pass, passport and to enter the United States visa.