The reason for silver oxide batteries is that they have an extraordinarily constant voltage over temperature and over their entire life. When electronic watches depended on the battery voltage, that was important. Modern digital watches have a quartz crystal oscillator in them and the frequency of that oscillator is not substantially dependent on battery voltage.
Lithium button-cell batteries have a very long life, but only under a constant discharge rate. If you use the backlight or alarm or chimes which result in sudden increases in the discharge rate, you will reduce the battery life.
Alkaline button cells have the highest life under higher loads which is why they're popular for hearing aides. Air-Zinc cells are pretty good for this but they have very poor shelf-life once activated. They also find a lot of use in hearing aides.
Just for completeness, mercury button cells have the most stable output voltage but the lowest life but are perfectly happy with an on-again-off-again load. They were often used in camera light meters where the load is very intermittant but a very accurate voltage is required.
My beloved Pentax Spotmatic II camera calls for a mercury button cell. When it went dead, I was heartbroken since the zinc-air replacements only last a few months no matter how you use 'em. Then, I discovered (via the internet) one store in American that still had three of the required mercury cells. I bought all three. The shelf life on mercury button cells is many, many years.