This topic has come up quite a few times over the years on this board. A lot of the discussion around it has mostly been others opinions. I found this neat little graph online (instagram) from the New York Times that compares the two. Now keep in mind one's location will certainly have an effect on which one might make more sense, even in what part of you own country you're in.
This graph is really meaningless and does not reflect the actual reality of renting vs home ownership. Renting is definitely useful for certain people, especially those who are younger or need to be mobile when searching for work. Not being tied down to one geographic location is very useful and it is the only thing that certain groups can afford. Home ownership comes with it's own set of benefits and responsibilities however. You are ultimately paying off an asset each month and will end up with ownership of a very expensive asset at the end of it, you're not paying for someone elses house. There is also the inevitable debate about the ability to "make yourself at home" as many renters are restricted in what they can do, but sometimes benefit because the landlord may have to keep a certain level of upkeep for them.