Two very different methods. The SpaceX approach is more expensive
Actually the SpaceX approach is cheaper. Cost in 2026 dollars to develop the Apollo rocket $280 billion (up to $300 billion), Starship $15 billion to date. The LEM alone $28 billion.
Artemis so far over $93 billion. That in spite of the first stage being a modified shuttle external fuel tank. The main stage engines modified shuttle main engines (some actual flew on the shuttle). Modified shuttle solid rocket boosters on the main stage.
Artemis 1 launch - $4.1 billion, Artemis 2 launch - $4.1 billion.
Starship twice the thrust (at least). Targeting fully reusable (SLS disposable except the capsule being "component level" reusable). Starship launch cost (estimated) $100 million (not billion) expendable and $30 million reusable (estimated).