A single Artemis launch costs $4.1B

Difficult to directly compare as the Orion spacecraft is designed for a lunar orbit mission, with a 21-day mission time, whereas Crew Dragon is a low Earth orbit capsule not really intended for maneuvers aside from "go up, go down." So you'd have to look at lifting capacity and then factor in your best guess as to how SpaceX would approach designing a TLI (trans lunar injection) capable spacecraft.

In many ways, Orion is Apollo Block III: what we would have developed if the Apollo program had continued to be funded. For better or worse.

To the moon costs are ~$31,500 per kg for SLS and ~$2,000 per kg for Starship according to:

https://everydayastronaut.com/sls-vs-starship/

Time will tell though as they are both in late stage development.

Edit: SLS vs Starship is the correct comparison to make. Spacex does not intend to use Falcon 9 or the Falcon Heavy for lunar transport.

So according to the article the cost breakdown is

> $2.2 billion to build a single SLS rocket, $568 million for ground systems, $1 billion for an Orion spacecraft, and $300 million to the European Space Agency for Orion's Service Module

SpaceX's alternative to the SLS would be Super Heavy (Starship's booster), but that isn't ready yet, numbers are mostly Elon projections. From the rate at which they are producing prototypes we can guess it's much less than 2.2 billion though. Falcon Heavy exists and costs about $150M per launch (costs as in: "that's what customers pay" [1]). It falls short in payload capacity, but for the first few Artemis launches you could conceivably do it with two Falcon Heavy launches each, totaling $300M. For the later launches you need SLS or Super Heavy.

For everything else SpaceX doesn't have comparable offerings. A Dragon to the ISS costs around $55M per seat, so $220M in total, but it's not really comparable to Orion.

[1] https://www.space.com/nasa-picks-spacex-falcon-heavy-launch-...