I tested the following free themes: phpBB, myBB, SMF, nodeBB and the following paid themes: xenforo, vbulletin, woltab.
Responsive vs not responsive
We faced many issues with

Bugs in themes of open-source forum apps
We bought phpBB, myBB and SMF themes. We didn’t find a theme as reliable as the Xenforo or Vbulletin theme. For example, some buttons were hidden or some were disabled. Many times, the discussion board was located 500 pixels below the top of the page. We saw broken links, missing images, hidden texts on those themes. Also, when we had to change something on a free internet forum theme, we had to get into the CSS very quickly.
I remember when I bought a phpBB theme, I tried to change its colors using CSS. I added !important. Then, even after purging the phpBB cache, the displayed colors were always the former ones.
On the other hand, the themes of paid forums like Invision, Vbulletin, xenForo had no broken links, missing images or disabled buttons. The Vbulletin and the Xenforo default themes are ready out of the box. You can change the color from a customization panel. Once again, the paid internet forum

The exception was with
We also bought phpBB themes from themeforest. One was called bulletin. We had to use “display: none” to hide a big block. We don’t like to use “display:none” for SEO reasons. Then, we wanted to change the colors of the themes and we added it to the custom.css file. After purging the cache and adding !important it still didn’t work. That’s the type of issue you never face with paid forum softwares.
Themes of free forum software are bad for SEO and readability:
We saw that plenty of themes from free internet forum softwares were not designed for SEO and readability in mind. For instance, there are plenty of SMF themes and phpBB themes with a header that is around 350px in height. It is just too much. There is a Google penalty linked to it. On the other hand, when you look at Vbulletin, Xenforo, woltlab forums you can see that valuable information is displayed right from the top of the page. For your information, Google penalizes websites with an empty space at the top with no data.
PHP errors
phpBB is 18 years old in 2018. I thought there would be no PHP errors anymore. I was wrong. Then, for some reasons PHP errors started to show up on every single page of a PHP forum software, then the error has been picked up by Google and I saw the following in the google results (see below). With myBB and SMF, I didn’t see any bugs as long as I stuck to the default theme. With

Usability
Before starting the review of paid internet forum
Upgrades on free forum softwares are dangerous:
Due to how the theme’s files are integrated into the internet forum softwares and since plugins are necessary to get important features like SEO friendly urls, updates can break phpBB, myBB, SMF installations. Themes and plugins may not be compatible after an upgrade of the core forum code. We witnessed this issue with myBB and phpBB.
For example, after upgrading to PHP 7.2, an error started to be displayed on every phpBB 3.2.2 pages.
Missing features and mandatory plugin installations:
We found no free internet forum applications with SEO friendly URLs like /this-is-my-topic/. This always required the installation of a plugin to get the title of a thread as keywords in the URL. There are SEO plugins. however, many plugins aren’t maintained by developers. It means many of phpBB, myBB, SMF plugins don’t work.
Because of this problem, if you have let’s say 10 plugins on your SMF or phpBB installation, it is advised not to upgrade the version of your SMF or phpBB otherwise, one of the plugins may stop working. For example, As I am writing this article, it is late 2018. Some SMF plugins haven’t been updated since 2015. Those plugins may work. However, someday, SMF may modify its files and the plugins may stop working.
Also, features that are delivered by default on every paid forum software aren’t always provided by a free internet forum software installation. For example, the user karma system (also called the reputation system) is no embedded in the phpBB default installation. the Nofollow option on external links isn’t a default feature of phpBB, myBB, SMF. The SEO friendly URLs aren’t a default feature of phpBB, myBB, SMF.
Paid forum softwares are ready out of the box:
I have found that Xenforo, Woltlab, and Vbulletin were ready to be used out of the box without looking for a responsive reliable theme, modifying CSS or PHP, installing plugins, changing colors. This tremendously speeds up the design and the maintenance of the brand new forum, because you don’t need to spend hours to look for plugins, installation of plugins, CSS and PHP coding.
Think about a potential migration
I have noticed that many webmasters of free forum software moved their phpBB, SMF or MyBB forums to XenForo or Vbulletin. Today, there is no import module to move from phpBB, SMF, myBB to XenForo or Vbulletin. Anyways, when your forum counts hundreds of thousands of threads and thousands of members, the migration is going to be a big issue. If you decide to move your data from a free open source forum installation to a paid forum installation, you will very likely have to hire a company to perform the migration and it is going to cost more money that buying a license of a paid forum software like Vbulletin or Xenforo.
Conclusion
1/ You have a community or you have a budget. Don’t waste your time and go for a paid internet forum like XenForo (paid)
2/ you don’t have any budget for a forum. You don’t have a community. Your community will never help to earn money. go for Simple machines forums (free).