What focus mode are you using? If you are using AF-A (Auto-Area), then the camera may not be choosing the focus priority you have in mind. It is usually biased to the closest object(s) in the scene. Set your camera to single-point autofocus and see if that doesn't improve things. I've owned a bunch of Nikon SLRs and DSLRs and the autofocus modules have been bang-on.
The autofocus mechanism can figure out which way to go to achieve focus so it can focus very quickly. Live view uses contrast detection on the sensor, but this method does not provide any information about whether the focus is out front or in back. Therefore it's slower.
Try single-point focus mode to rule out operator error.