I understand that mechanical, fuel, ATC etc... would be different between aircraft types on the same route but I am confused by some other differences.
I have two flights on the same route each day. Flight 1 is an A321 and Flight 2 is a B739ER. Both flights have 6 cabin crew and 2 flight crew.
On Flight 1 (A321)
Cockpit- $685
Cabin Crew- $662
On Flight 2 (B739)
Cockpit- $685
Cabin Crew- $651
My B739 Cockpit crew have a higher weekly salary than A321, yet show up as costing the same. All cabin crew have the same wage, yet the A321 cabin crew are slightly more expensive.
There are also differences in overheads. A customer on the B739 costs only $79 to service in Customer Relations, yet that same customer on the A321 costs $81. The administration for the B739 flight is $412, for the A321 $423 (how things like HR or payroll would be different for the A321 I'm not sure!).
Some other things which you'd expect to be the same are the same- for example it costs $273 to check in a passenger on an A321 and $273 to check the same passenger in on B739.
Why? Are costs somehow equalled out across expense categories and flights?
These costs that you mention (mostly salaries) are all paid once a week, not per flight. Therefore, in this calculation they are divided over all flights that are scheduled on that aircraft, and of course longer flights get a bigger share of the costs. So the values that you see there depend on what other flights are scheduled with that aircraft - in your case, it seems that the B739 has more and/or longer flights that the A321, since its costs per flight are lower (in other words, the B739 is used more efficiently). If you would sum up the Cabin Crew costs of all the flights scheduled for a week, you would get the same value for both aircraft.
Example: Assume the B739 flies two routes daily, one that is 400 km (X-Y), the other is 600 km (X-Z), and the A231 flies only X-Y (400 km) twice a day. Let's say the cabin crew of one aircraft costs 7000 € per week, or 1000 € per day. For the B739, since the flight X-Y is shorter than X-Z, it would only get 40% of the costs (400 €), and X-Z would get 60%, or 600 €. The A321 however flies X-Y twice, so each flight gets 50% of the cost, or 500 €. That's why the crew cost for the same flight can be different on different aircraft (even if they are the same aircraft type!).
The check-in costs, on the other hand, are paid for every flight separately, so they don't depend on any other flights. Therefore they are the same for both aircraft. The same goes for catering, for example (assumig you use the same service profile). These kinds of costs are listed as "Variable Costs" and "Flight-related costs" on the flight information page.