Twitter has revamped its friend-finding features today to make it easier for Facebook friends to follow each other. However, the feature isn’t completely working and the reason why is unclear.

First, how it’s supposed to work. If you’re coming from Twitter’s site, you’re presented with the option to sync with Facebook by clicking through to add Twitter’s Facebook application. You’ll need to install the app, thereby providing Twitter with access to your basic information as well as your personal interests.

The app then lets you sync your profile photos between the two sites, as well as status updates from Twitter to Facebook (which the app has allowed you to do for years). You’ll also get the option to find friends on Facebook who have also installed the app; if your Facebook friends are on Twitter but have not installed the app, they won’t appear here.

The app shows you which Facebook friends you’re already following on Twitter, and which ones you haven’t. If you want to follow new people, you can either do so directly or else create a list. The latter option gives you an easy way to see what all your tweeting Facebook friends are up to, and it defaults to private, meaning that unless you make the list public, those friends won’t know that you’re following them.

Right now, however, the find-Facebook-friends functionality isn’t working. At first, Twitter described the problem as an intentional block from Facebook, but now both companies are saying that they are working together to solve the problem. Given that the Twitter app is using the Facebook platform in the same way as many other third parties, we expect the problem — whatever it is — to be resolved. In the meantime, Twitter is has stopped directing users from its site to its Facebook application.

The fascinating history between the two companies adds a new dimension to this product, and its problem.

Twitter has emerged as Facebook’s leading social service rival in the last couple of years, although Facebook is more focused on private, real-life connections and Twitter is more focused on public sharing (on a related note, it’s not clear why Twitter is asking for Facebook users to provide it with their personal interests). Facebook tried to buy Twitter in late 2008 and started to compete with it more directly — even altering its algorithmic news feed to be a raw stream of status updates in early 2009, although it then switched back later last year. In hindsight, Facebook founder Mark Zuckerberg tells us that he “paid too much attention to it.” Check out our recent interview with Zuckerberg for more on that.

Although Twitter’s traffic has been climbing slowly for the last 12 months or so, it continues to expand around the world — and it also appears to have attracted a significant number of Facebook users. A recent update to Facebook’s publicly available application traffic showed Twitter (along with a wide variety of other apps) to be far larger than previously visible. It has 6.7 million monthly active users, according to AppData, rather than the few hundred thousand it had previously shown.

Assuming the Twitter app works as intended, the result should be more Facebook users getting more value out of Twitter. While this is unlikely to affect how people use Facebook, the two companies are both actively evolving their products; whether or not they become more direct competitors is something that even they appear to be unsure about. Regardless of how the companies see each other, many users themselves seem to be getting value out of both: Twitter tells TechCrunch that the ability to find tweeting Facebook friends has been the number one support request for some time.