Replacing with a 16v verse 10v may no make a difference in how long it lasts. The cap did not fail because it was a 10v cap, if failed because of the ESR increased over time. ESR is the the equivalent series resistance, effective a resister in series with the capacitor. The higher the ESR valve, the more heat it produces inside the capacitor, the heat leads to increasing the ESR which leads to a higher temperature. Also the higher the ESR the less effective the capacitor is at filtering ripple current, especially high frequencies.
Replacing the part with a 10v low ESR part is better than using a 16v part with a higher ESR. In the modern day switching power supply, it is all about using low ESR parts intended for high frequency switching power supplies.