I play SHBH and have a good slice. On that side, I can drop either high balls (step in to take it early, shape for a topspin backhand but then change grip, break wrist and cut it, like in the Gilbert video) or low balls (shape for a normal low sliced backhand, and just shorten the swing and put a bit of sidespin). But in either case, I generally go down the line and move up to cover a return, very seldom go cross-court and open my own court up.
On the forehand, I seldom drop from the back (and when I do, always down the line). But I often drop / dink it over when I'm reaching for a shorter-but-wide forehand - if my opponent has played a cross-court forehand from the back of his court and/or wide, that's the place furthest away from him, and I can move up to the net to cover that side of the court, so forcing him to do something with his pick-up.
About the only time I drop cross-court is in doubles, on second serves. Often, the server will stay back after those. I step forward to take the ball early and high, which locks the net person in place, and then just break the wrist and slice cross-court to the tramlines, forcing the server to run in and hit a weak upwards shot for my partner to put away.
