as for the "noise" of play on various tables, that depends heavily on many things...
the accoustics of the floor/room, the cloth, the cushions, what the rails are made of, how the slate is mounted to the frame, the ball return construction, etc etc...and believe or not, a thicker/larger slate actually has the potential to create more noise.
the source of the noise, of course, is the ball impacting against various surfaces (and actually rolling across the table). the slate (and the table itself) acts as a sounding board or 'speaker' - that carries and amplifies the impact vibrations. the 'more solid' a table is in its construction, the easier it is for the vibrations (and sound) to be dispersed through a table and out into the room.
can noise be prevented or reduced? yes, to a certain extent it can.
(although you obviously cant do anything about ball-hitting-ball noise)
but a thicker slate wont help much, if at all, and may even make it worse.