It would be fair to say, before I get into picking into the app too much, that I really like the standard Facebook app. I'm sure that there are plenty of ways that you could improve upon it, but the overall layout is very easy to navigate and doesn't make me want to hurl my phone in disgust. With one button I can access my news feed, check-in to a place, see my friends, my groups, and my photos. It's not perfect, but it is really quite nice.
Not satisfied with the status quo, Facely really steps out of the box to create an experience that is the same in many ways, but subtly different. Other than the obviously obnoxious fire red theme (that you can thankfully turn to "Facebook Blue"), the main change is that everything is available to you from the main screen. All squished up into the top of the screen is a button for home, profile, friends, inbox, search, back, chat, notifications events, and places. Since the news feed is the main page, all you have to do is scroll down and all the menu stuff goes away.
Aside from the menu system change, the biggest differentiating factor is that Facely looks much more like the desktop version than the official Facebook app. Info screens are laid out as they are on the desktop, the chat screen actually looks like a chat screen, and the option screens all look more desktop than mobile. What impresses me the most is that the pictures throughout the app, particularly the ones linked to posts in the news feed, all come out in full quality. If someone posts a YouTube video, you'll actually see the hi-res preview of the video instead of the crummy distorted image that pops up in the official Facebook app. It may not seem like a big deal, but once you see Facely it's hard to go back.
The question that people will have to ask themselves is whether or not they are willing to pay for Facebook. While I do think that Facely is a nice app, it is only marginally better than the official, and free, Facebook app. If you do plan on buying Facely though, just know that it is a good app with a solid UI.