Hi DP,
I'm one of the believers in a "quiet hand". That is, the quieter the hands (i.e., no unnecessary and uneconomical movements at the keyboard), the more efficient and effective one is in accomplishing the technical and musical goals set out by the composer. But before you conjure the image of rigor mortis, let me explain further.
First, to achieve quiet hand motions, the entire playing mechanism must be relaxed. As Colette aptly points out above, tenseness and stiffness kill any pianistic endeavor. Relaxation must be present in the torso, shoulder, upper arm, forearm, and wrist (the fingers have to be somewhat taught to articulate properly). The wrist has to be free floating, supple, adaptable and fluid in its motions. When some part of the mechanism becomes tense, the wrists and fingers will then desperately try to do double work to compensate, but the result will be substandard every time.
Some examples to illustrate: If you're called upon to play fff, that starts with the torso. You'll bend forward toward the keyboard. If you are playing sonorous chords, that will be chiefly governed by the upper arm, which will influence the forearm in applying controlled arm weight in the situation. If you are doing a rotary motion for a tremelo or doing stacatto octaves, etc., the wrist will be predominant. In playing legato and light staccato, the fingers will be essential contributors. Yet in portato, the forearms and wrists will come more into play again. But none of this can be accomplished if, for instance, you're shoulders are tensing causing stiffness and pain there, thereby hobbling the rest of the playing mechanism.
When I said "quiet wrists", generally speaking they'll be level with your elbows and will not be engaged in bumpy or jerky motions. Having said that, there are some important exceptions. If the two hands are playing in extremely close quarters like overlapping, one of the wrists (the hand that is impinging on the other hand) will be raised a little to accommodate. Or, when playing the black keys, the hand will be thrusted forward slightly to be able reach those notes better. Or when playing with arm weight in striking a sustained chord, the wrists will sink in the keys very slightly as "follow through" that is not different in principle from following through with the raquet after hitting a tennis ball. Or one hand might have to cross over the other. All of this is choreographing the hands, much like dance steps, to make sure execution is as smooth and seamless as possible.
Have you ever watched conductors? Most often the best conductors are not those given to large, frenetic, and dramatic motions. Rather, the real pros are those who can muster the forces of the orchestra with very economical motions. For example, while Leonard Bernstein would be jumping off the podium into the air, Antal Dorati would barely move a muscle, and yet would draw an incredible effect from the entire ensemble! It's the same with pianists and how they employ their wrists along with the rest of the playing mechanism.
Incidentally, on fingers, long fingers (I have them too) are a decided asset in playing certain composers like Rachmaninoff who also had large hands like us. I never found large hands to be at all helpful in Mozart however. When I was a student, there were others with tiny hands who could always play rings around me in that regard.
As years pass, and once you have paid your dues in proving yourself as a "well-rounded pianist", you might then tend to specialize in the music of composers whose music you not only admire and most enjoy, but whose styles of writing best falls under your hands too.
I hope this helps.
Topic: What is wrong with me Hands ???