I have a blog, should I install a forum in folder or subdomain?

First of all, from a SEO point of view, we tested it and they are treated equally by Google (verified in 2018). 

Advantages of subdomains:

It is great if at some point you classified ad board gets so big so that you need a new web hosting server to host it. You can install the blog and the forum on two separate servers. Since internet forums get lots of visits, it is also better to separate installations. 

People can find the forum using a subdomain. On a smartphone, it is always easier to find dots than slash characters. For example, forum.domain.com is easier to type than domain.com/forum/ . On the android keyboard, the / character is located on the second keyboard after clicking the “123” button of the 1st keyboard. On the other hand, the dot is located on the 1st keyboard. Consequently, it is easier to type a URL with a subdomain. 

The most famous internet forum and classified ad board Craiglist.com uses subdomains to target a location like newyork.craiglist.com , london.craiglist.com, paris.craiglist.com

Advantages of subfolders:

To install a forum in a subfolder is easier than installing the forum in a subdomain. For instance, if you run WordPress, you can install a plugin and your forum is up and ready very quickly. On the other hand, if you install a subdomain, you must add DNS records. 

You don’t need a new SSL certificate for a subfolder since it is a subfolder of the root domain.