As minimum feature size shrinks to a metal pitch of 21 nm, the current extreme ultra violet (EUV) lithographic tool with a numeric aperture (NA) of 0.33 will face resolution limit for some critical layers. High NA (0.55) EUV with anamorphic optics or EUV double patterning (DP) at 0.33 NA are being considered for the next generation of lithographic technology. Both the high NA EUV system and EUV DP will enhance resolution relative to current EUV single patterning (SP). Nevertheless, in order to be able to compare EUV DP and High NA EUV processes, important lithographic factors including image contrast, mask three dimension (M3D) effects, process variation band, stochastic effects and local critical dimension uniformity need to be investigated to understand their contributions to process variations. This study was carried out using rigorous lithographic model simulations in Sentaurus Lithography, where strong M3D effects in EUVL are computed physically. We have simulated patterns with both isomorphic and anamorphic optical proximity corrections (OPC) using the rigorous model. The study focuses on 3nm node Via layer designs. These vias need to connect to metal features which have pitches of 21 nm. Simulation results using 0.33 NA SP, 0.33 NA DP, and 0.55 NA anamorphic SP are presented. The benefit of using an alternative mask absorber and a thinner resist as well as the impact of stochastic effects have also been explored. Although a 0.55 NA EUV is expected to produce a superior image to 0.33 NA EUV and to have less impact from overlay errors and stochastic effects, an analysis of process margins of 0.33 NA EUV SD and DP versus 0.55 NA anamorphic systems helps to better understand the benefits, challenges and optimal insertion point for introducing High-NA EUV.