Those operating costs are largely the same irrespective of whether the carrier is tied up at port or deployed at sea.
Sailors still need to housed, fed and clothed; air crew still need to fly and train etc. USN carriers are all nuclear, so fuel costs for the 'boat' itself doesn't really change.
The biggest cost difference will be fuel costs for the escorts, but that's just small peanuts compared to all the other costs associated with owning the ships. At least as far as the USN is concerned.
For China, long range deployments would cost more per mile, since its ships are all conventionally powered, and they lack foreign bases so all the supplies and fuel need to be carried by replenish ships. But then, it costs a lot of money to run foreign bases.
At the end of the day, to sum up, think of it like this, the USN is like someone who has paid a premium price for an unlimited calls contract, whereas the PLAN is on a (much smaller)pay as you go contract.
The USN has to pay a huge annual fee irresptive of how many calls it makes, whereas the PLAN gets charged a small fee for each call it makes.
As such, it makes sense for the USN to make as many calls as possible, while the PLAN needs to be a lot more rational about whether or not to make a call.
Ultimately, if the PLAN find that they have commitments that require them to make a lot of calls, it might also be worthwhile for them to move to a unlimited calls packaged, which we are starting to see with recent deployments in the Indian Ocean and rumours of nuclear carriers.
But the downside of that is that the navy may be tempted to help create tensions to justify the high frequency of deployments, to justify the huge fixed costs, rather than acccept cost cutting, as we are seeing with the USN to some degree.
Peace and stability are not good for a service with massive costs and no justifiable need for its vast fleets at a time or shrinking defence budgets.
