If we look at the last 15 scheduled airlines in the FLIGHT_ON_TIME punctuality list, we find JET2 at number 27, with British Airways at number 26, Easyjet at number 22 and Ryanair at number 20. Below JET2 at number 28 is Emirates and at 29 we have Qatar Airways.
Considering the competing airlines and their brand new fleets, JET2 are doing very well to maintain their position among such strong competition.
The long haul carriers you mention operate from large hubs and will often delay their own flights for connecting passengers. You need aircraft dispatch reliability figures if you wish to compare old for new, which you will be hard pressed to obtain.