I checked for a 1.2 mile ride just now (23:52 on a Sunday night); it was $9.32 for a Waymo, $12.49, discounted to $9.66 for a Lyft after Lyft pink, and $11.32 for a Cruise. I don't have Uber access after using curl against one of their endpoints using my account, so I can't say what that would have cost.

So, pricing is dependent on various opaque factors, but it's not universally more expensive. Cruise used to be free, but they finally started charging for them.