Will it run one of those screens, yes. Will it run at 144hz in games, depends on the game. Need to go game by game. CSGO at 144, most likely. Something heavier, probably not unless you run at low settings.
To answer your question, yes this system will run 144hz with no problems.
Between the two monitors it is pretty much identical, Zowie is definately far more renown than Viewsonic in terms of the E-Sports business. It depends what is within your budget, personally I would go with the viewsonic as it does everything the Zowie offers but with more peripherals to go with it (e.g the integrated headphone stand). If that is no concern to you then go with the Zowie as it is slightly cheaper in that regard.