High drain batteries risk burning the movement out.
Hi Voltage risks burning out a movement, not high drain
Take theses 2 batteries.... SR920W (370) & SR920SW (371) here's what all those letters mean
S = Silver
R = Round
9 = 9.5mm Diameter
20 = 2.0mm thich
a W on its own means is complies with IEC 60086-3 an international standard for these types of batteries....... no letter between the numbers and this w means the battery has organic electrolyte in it. a "S" means it has sodium hydroxide electrolyte in it. both batteries will supply 1.55volts with an even current. its only the chemical make up that means if a watch is running an alarm, light or stop watch the battery is able to maintain a higher drain more constantly, but may not necessarily last longer under normal load.
A SR920SW will not damage a watch originally fitted with a SR920W or vice versa, But a SR920W in a watch with additional functions will drain much quicker (if these functions are used regularly) so you customer will be back unhappy!
If you remove any battery from a faulty clock & replace it with a cheaper one & the clock begins to work, then this would ONLY suggest to me that the terminals have a thin layer of potassium carbonate on them & putting the new battery in has rubbed this layer off enough for a good current to make is way back to the clock. A good clean of these terminals & any brand or type of cell will work. (IMO)