Does T-Mobile or AT&T work in Ecuador?

No! This is a common mistake. Although Ecuador uses the US Dollar, it is an independent country and NOT part of any US domestic plan. Most home carriers (like AT&T, Verizon, T-Mobile) will charge you expensive international "Day Pass" rates (e.g., $10-$14 per day). A Ti Porto in Viaggio eSIM is a one-time prepaid fee that is significantly cheaper.