How long have you been playing the game? It takes a long time to become a good online player (at least for me it did). It's significantly harder to hit against a real person than against the CPU even on legend. Learning how to pick up on tendencies and working yourself into good hitting counts takes a lot of experience. And also, learning what pitches you can hit well and make good contact on is huge. If you can do that you can look for that pitch until you have two strikes and don't swing unless it's there. For me, I can't hit low and in so I just don't swing at it unless I have two strikes.
As for the monitor argument, does it make a difference? Yes but I wouldn't say it's significant until you're playing on legend. Last year I played on a 65" TV and made World Series numerous times. I switched to a monitor this year and have only made it once so far so take that for what it's worth I guess.