The big cue ball used to make a huge difference. It affected everything from drawing the cue ball, cue ball speed after contact, to deflection angles. Shooting at an object ball frozen on the rail was quite different as you had to compress the rail in order to get to your contact point. Plus you had to have a good kill shot to control the big ball's bounce off the rail. The break was also affected. More mass, more action.
With bar tables now having a "normal" cue ball the the biggest current difference between the bar box and the big table is that one can make much more aggressive shots on the smaller tables;shots such as banks, caroms and combos. These are shots which big table players tend to try to avoid or play safe on but which true bar box players see as high percentage shots and play shape for. - Tom