The beeping is normally just a focus lock notification setting in the camera. Typically there is also a color change of either the focus point in the view finder or a color change of the focus square on the LCD.
Viewfinder uses Phase Detect Auto Focus on a dedicated sensor which can detect when focus is achieved more quickly, but generally requires more light. It should generally avoid focus hunting (where it goes in and out.)
Live view on the other hand is putting light on the image sensor rather than the AF sensor(since the mirror is up), so it has to focus by adjusting the focus and seeing if contrast gets better or worse (looking for sharp edges). since it is a trial and error approach, it can end up hunting back and forth, it also makes it slower, though it can generally work in lower light. It is also generally slightly more accurate, but PDAF is generally preferred for speed.