Welcome, p123! Always great to see new members here!
Xenforo and phpBB are two different animals, ultimately. Yes, they're both forum software, but phpBB is freeware, developed and maintained by volunteer staff on their free time. There's nothing wrong with that, and it certainly doesn't equate to a bad product, but it does typically mean that releases are slower paced and bug fixes come out at a pace not quite expeditious, with security fixes released within a day or so of being reported. Xenforo is developed by full-time developers and bug releases typically come quickly and en masse, with security fixes coming within hours of being reported. The level of development and innovation is also much higher in a product like Xenforo, with features and code updates coming typically years ahead of freeware options simply because of the nature of freeware development (not saying there aren't freeware or open source products that don't have full time teams, there absolutely are, but in the freeware forum software market, it's mostly volunteer developers working in their free time). As far as cost goes, well, Xenforo is, as mentioned, a paid-for product, so yeah, it's more expensive to operate than a phpBB install, which is free to download and can be installed on a free host if you find one with decent specs, whereas Xenforo costs $160usd up front and $55usd/year for continued support and update access, not to mention a fair few of the add-ons are premium add-ons and come at a premium price, so there's the possibility of added costs there, as well.
It's about investment, ultimately. If you can get the level of functionality you want out of the free market, take that route, by all means! There are some great options available, like MyBB, Flarum, Vanilla, and so on. If, however, you're looking for a little more out of your community and don't mind spending a bit to get there (and if you've ever delved into the website game to a big degree, you'll realize that this is not exactly a lot of money compared to what some people and companies spend), then the paid market is the better option overall.