It largely depends how fast both city is growing now. If both grows at the same rate they did between 2010–2015 (City of Manila - 2015 - 1,780,148 at 1.43%; Davao - 2015 - 1,632,991 at 2.3%), Davao City will marginally surpass the City of Manila’s population by 2026. Using the same population growth rates, both will reach more than 2 million by 2024.
Davao City can actually become the second largest city at an earlier time considering the attention (and investments) it has been getting as President Duterte’s hometown. Or it could be a little longer if the good news generated by Manila Mayor Isko Moreno entices people to return to the capital. We can better gauge this when we see the results of the 2020 Census.
Update (July 2021):
The results of the 2020 Census has been released. The City of Manila’s official population count is now 1,846,513 and Davao City at 1,776,949. Between the two censuses, the former added 66k and the latter 143k. Assuming the same number will be added in the next 5 years, Davao City will be marginally larger than the City of Manila by the next Census. And both cities won’t reach the 2M milestone just yet.