If this is an industrial application, ANSI standards apply.
Generally, you want to stop motion in an emergency condition.
M-G sets would continue to run, but motor starters would be taken out, ie drop out and stopped and have to be reset depending on the E-stop circuitry.
The sequence of operation of the machine is a good way to determine what would get stopped in an emergency condition. Whereever the operator has access to the maching is where an E-stop should be placed.
For example on a rolling-mill where you have 4 or 5 people running the machine you would want to provide E-stops where they are accessible to all peronnel, when these machines are stopped, in and E-stop condition the hydraulics cannot be stopped you loose the coil on the payoff reel and take-up reels pressures and the mill stands would open causing a worse condition than the actually Emergency itself.
You would want the mill to maintain tension on the steel so as not to lose your place as it were,(DC armatures would dump their energy into the DBs and mechanical brakes would stop the whole process) but you want the machine stopped. So all motors, moving parts have to be stopped together. (Otherwise you wind up with what was known as a 'Coble' or a wreck where the 100 feet of sheet metal turns into ribbon candy, or looks just like it.)
The placement and sequence of E-stop operation is done by engineering. or should be big machines need to be well controlled.
The E-stops are usually set up in series so that if one is pushed the E-stop circuit will open/drop out if done by relay or computer or they used to use the Push to stop and pull to reset.
Be extremely carefull installing them done wrong can be catostrophic.