Hi,
I read that the battery life is good for about 60minutes of 4K recording (X3) on a full charge.
Does it also applies to 1080P/60fps?

It is my understand that you are correct.  

I thought that 1080p would give longer recording when there is less prosessing.

the battery provides multiple control voltages to OSMO
mainly for gimbal motor function and aux for processor support.
processor support is secondary to gimbal functionality. without gimbal function, the workflow is compromised.

Thank you for the clarification.

Does anyone know of any resellers in the USA that has OSMO batteries in stock for sale?