There is no simple answer to that question. Both are capable, modern, supportable systems for generic web serving. If you are not expecting huge traffic levels (the nature of your question makes me think this is just a small personal/hobby/learning type thing), both should work equally well. If you have more specific requirements, i.e. something other than a simple generic web server, that could favour one over the other.
Since you are asking on the FreeBSD forums, clearly FreeBSD is the better choice. Other forums may have alternative bias.
Nginx or Apache on FreeBSD get you started very fast and offer just about everything you could ask for. It's only when you get to very very large deployments that you actually have to start taking a closer look at alternatives and evaluating if your current solution cuts it performance or maintainability wise.
I actually prefer both operating systems very much, so since you're asking a somewhat beginners question I'll approach this as such: From a new user perspective I'd say that FreeBSD is likely the better choice. If you check the OpenBSD goals you'll notice some specific things:
Provide the best development platform possible.
Greater integration of cryptographic software.
Focus on being developer-oriented in all senses, including holding developer-only events called hackathons.
In short it's fair to say that OpenBSD focuses on security and development. So some aspects of the OS might be obscure for you if you're not already familiar with development. That's not saying OpenBSD can't cope, absolutely not, but the learning curve can definitely be harder, provided that you're indeed a new user.
FreeBSD has a somewhat broader perspective. The mission statement is basically "The power to serve" and if you want to know more about what FreeBSD has to say about itself they're basically directing you to other sources of advocacy because that is the only fair thing to do.
So my 2 cents on all this: FreeBSD is an operating system which is provided and maintained by a massive group of highly motivated individuals who all try to provide the best experience possible (but the same can be said about OpenBSD!). This experience can range from developing new user friendly utilities such as pkg(8) (the 'new' (it's been in use for some years now) package manager)) but also shows itself when you look at the FreeBSD handbook and the other massive amounts of available documentation and even the FreeBSD community (now hinting at this forum).
That's why I think that FreeBSD is more likely to provide an easier experience if you're just starting out with all this. The power to serve (FreeBSD) vs. Only two remote holes in the default install, in a heck of a long time! (OpenBSD).
Different operating systems, different communities, different approaches but all awesome.