I have been playing Civ 5 for a while but am new to religion. If I destroy a Civ and captured its holy city, should I try and convert it, even though the other civ's religion is spread further, or let both religions coexist?
Unfortunately, this is kind of a difficult question to answer, since it hinges on a lot of factors. First off, what is your religion like, bonuses-wise, compared to the religion in question that this city is a Holy City of? It may be more beneficial to this city's growth and purpose even if you're not enjoying Founder benefits from its followers.
Raven Dreamer has already discussed how difficult it is to neutralize a Holy City's internal pressure - in short, you need six cities in pressure range that follow your religion to keep it on your side. Can you take the Happiness cost that maintaining this would incur? Do you have Missionaries/Great Prophets that can establish this network of pressure? If not, you may not be able to flip it to your religion permanently.
If the city isn't a Capital, it may be worthwhile to just raze the city in question and create a new city at the site to claim it for yourself without that Holy City taint. Yeah, you'd have to rebuild the city's infrastructure and citizenry, but at least you're not dealing with the religious pressure.