Hi Harikiranjeet, as far the difference is concerned they are different in geometrical shape and also with respect to irreduicable Brillouin zone along the k vector path. Simulation is you have to choose what type of crystal you want and accordingly create the defect to create any sort of waveguide. Well I would say the hexagonal arrangement is much better for propagation of modes and output power is significantly better and thus the loss is.
Thank you