After thinking about this for a while (and actually allowing the Daylight spell to adversely affect a Vampire earlier in our current campaign), I think that I have to go with the side of the argument that states that the Daylight spell is not the equivalent of sunlight.
I came to this conclusion for several reasons:
1) The Daylight spell does not mention sunlight.
2) Both Sunlight Sensitivity and Sunlight Hypersensitivity both explicitly mention "sunlight", not daylight.
3) The name Daylight implies "light of the day", but in reality, this is just a spell name from earlier versions of the game.
4) The 3E version of the game stated "Despite its name, this spell is not the equivalent of daylight for the purposes of creatures that are damaged or destroyed by bright light.". Although that sentence is no longer in the spell, that's how the spell has always worked.
5) There is a spell called Sunbeam that is explicitly designed for this function. The light is sunlight.
6) The 3E version of Sunbeam was explicitly designed to harm undead creatures harmed by bright light.
7) Daylight is a 3rd level spell. Sunbeam is a 6th level spell. The version of the spell that harms vampires should be the higher level one that explicitly states that it is sunlight and explicitly states that undead get a disadvantage on their save.
So from what I can tell, the 3E version of Daylight did not harm undead and the 3E version of Sunbeam did harm undead. It is not unreasonable to maintain this interpretation in 5E, especially considering that the 5E version of Sunbeam does explicitly give this functionality and the 5E version of Daylight does not.
Note: Having said that, only Druids and Wizards get the Sunbeam spell. So, I could see a given DM allowing Daylight (which Clerics and Paladins get) to harm vampires due to motif. But I do think that a 3rd level spell is pretty low level for that amount of umph.