It depends entirely on where your city is and where it gets its energy.
The Electricity Map has live energy data for the Carbon Intensity of the electricity supply. Right now, the CO2 intensity of the electricity supply in grams of CO2 equivalent per kWh (gCO2eq/kWh) across the world is:
- 319 gCO2eq/kWh in the UK
- 28 gCO2eq/kWh in Norway
- 509 gCO2eq/kWh in the USA
- 800 gCO2eq/kWh in Australia
I understand the UK is mostly using gas powered electricity generation, Norway uses mostly hydro-electric, and the USA relies on coal.
We're going to compare the CO2 emissions per km for the different vehicle types in different places. The energy efficiency of electric buses is around 1.335 kWh/km, which amounts to the following emissions in the above mentioned countries:
- 426 gCO2eq/km in the UK
- 37 gCO2eq/km in Norway
- 680 gCO2eq/km in the USA
- 1060 gCO2eq/km in Australia
The CO2 emissions for a regular diesel bus are around 1077 g/km, according to this paper.
Switching to electric buses in most countries could avoid between 400 g/km to 1000 g/km of CO2 emissions compared to diesel. In Australia the difference in emissions between diesel and electric is only about 20 g/km.
At this point I notice that you mention "aging diesel-fueled buses". There have been great developments in diesel fuel efficiency in the last few decades. Your city's buses might have emissions a lot worse than the quoted 1077 gCO2eq/km. So even replacing the aging diesel buses with modern diesel buses might reduce emissions by 50%.
Furthermore, it's seasonal too, in the summer the UK's CO2 intensity was as low as 120 gCO2eq/kWh because of solar power and less demand for heating.