Flow and noise solutions of the two Large Eddy Simulation (LES) approaches are evaluated for the jet flow conditions corresponding to a benchmark co-axial jet case from the EU CoJeN (Computation of Coaxial Jet Noise) experiment. The jet is heated and issues for a short-cowl axi-symmetric nozzle with a central body at a transonic speed. The first LES method is based on the Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) scheme, for which implementation features include asynchronous time stepping at an optimal Courant-Friedrichs-Lewy (CFL) number, a wall model, and a synthetic turbulence inflow boundary condition. The CABARET LES is implemented on Graphics Processing Units (GPUs). The second LES approach is based on the hybrid 2 Reynolds Averaged Navier-Stokes (RANS)/ Implicit LES method that uses a mixture of high-order Roe and WENO scheme and a wall distance model of the Improved Delayed Detached Eddy Simulation (IDDES) type. The RANS/ILES method is run on an MPI cluster. Two grid generation approaches are considered: the unstructured grid using OpenFOAM utility "snappyHexMesh" (sHM) and the conventional structured multiblock body-fitted curvilinear grid. The LES flow solutions are compared with the experiment and also with solutions obtained from the standard axi-symmetric RANS method using the k- turbulence model. For noise predictions, The LES solutions are coupled with the penetrable surface formation of the Ffowcs Williams-Hawkings method. The results of noise predictions are compared with the experiment and the effect of different LES grids and acoustic integration surfaces is discussed.