I have 2 bikes: A Specialized Hardrock, and a Giant Boulder SE. The HR shifts very smoothly. When I shift from 1 gear to another, it responds precisely, very quick and with hardly a sound. However, my Giant is different. From the day I bought it new, when I shift it, it sometimes takes a couple pedal strokes before it responds, and it grinds sometimes going from one gear to the next. I've attempted to adjust the deraileur using the limiting screws, but that just made it throw the chain if I turned the screws too far in one direction, or it wouldn't shift at all if I went too far the other way.
I should add that both bikes use the same deraileur component group, which is Acera. I would expect that they would work the same, being the same quality. I doubt the bike brands being different would affect anything. Right? So is there any other kinds of adjustment I could make to make it shift more precisely?