The slots you pay for when you create a new route are always the same price regardless of aircraft.
However, there are other variables like if it's a peak hour that affect the price of the slots. You can see these from the small i icon next to the slot cost when creating a new route.
Route and landing fees (visible on income sheet) do however depend on the aircraft, and expecially it's weight. For example, you pay more for a B737 with +10tn MTOW than a 737 without it for each landing the aircraft makes on an airport.