What's better, setting up a dedicated server on my PC, or hosting coop via Steam? Or is it the same?
Given the information you provided, a dedicated is better. As I believe only 4 players is available, before crashing and errors, in the "single player, coop" client.
This also opens up that in the event you can't play, you can leave the dedicated running on your own machine and jump in when you please.
Personally I can't justify the server rental cost if my own pc can do everything.
Things I look at are, the time frame everyone is on vers when they aren't. So example, say you pay the monthly fee, but out of 30 days, only 4 total days are utilized.
It's not a viable option, in my opinion. Again given you can freely run the server on your own pc. Allows more modding freedom.
Rental servers, of those I have helped, they have been limited to additional file size limitations. So if the server itself is 4 gigs, and the server size limit is 5 gigs, once you start modding that file size starts adding up. As well as some mods do not work on rented servers. No matter which method. I spent 12 hours trying to help a user and the end result was the same. The server host was blocking file access and would not allow unless it was through official channels. Steam workshop.
Hosting a dedicated locally allows free range.