Blue Origin's lunar architecture is designed for a maximum of twelve moon landings per year for the Blue Moon Mk2 without using Orion and the same $4 billion budget per Orion+SLS flight.

SpaceX's architecture requires a second cislunar starship for the return trip. That will mean at most four moon landings per year and even that is optimistic. The large size of Starship makes return trips and lunar refueling really unattractive. If SpaceX wants to compete they will need to build a dedicated cislunar vehicle.