4.1 is a pinned API variant with the improvements from the newer iterations of 4o you're already using in the app, so that's why the comparison focuses between those two.

Pricing wise the per token cost of o3-mini is less than 4.1 but keep in mind o3-mini is a reasoning model and you will pay for those tokens too, not just the final output tokens. Also be aware reasoning models can take a long time to return a response... which isn't great if you're trying to use an API for interactive coding.