Features: Unread posts. This isn't a huge advantage with zhpmafia because you can use the new posts button, but on BF.c it saves a ton of time because it pulls the newest posts from all forums. I catch some stuff that I wouldn't normally see otherwise.
The participated tab is great because it grabs any threads in which you've participated and shows any new posts so you don't have to subscribe to threads and deal with all of the email.
Much easier to read, browse, and post than the mobile browser.
Ability to add a specific forum to your favorites list for easy access. Helpful for e46 forum on BFc. Will become more useful as zhpmafia grows in users and posts.
Usage:
For zhpmafia, I mostly work off of the unread post tab. For BF.c, I check the participated tab first to see if anyone has responded to a thread that I've posted on, then I browse the unread post list to see if there's anything of interest, then I move on to the e46 forum and browse those posts.
Don't know if any of that helps. If there's something specific you're looking to do or a specific problem, ask away and I'll try to help.
Of course, this is all predicated on the fact that you were able to locate the forums and login via Tapatalk.