If you look at FMDB you should see the answer.
FMDB is written in Objective-C and has an OO design. The sqlite API is written in C and is very procedural. FMDB uses Objective-C memory management, sqlite API doesn't.
If you're a competent Obj-C coder you can learn FMDB in a few hours. It's easy to use and has very few gotchas. The sqlite API is more complicated.
Integrating sqlite API code into an Objecive-C app is doable but will engender some pain. FMDB will fit into your Objective-C app very easily.
I've definitely been more productive and wrote code faster with FMDB than I would have if I used the sqlite API directly. If it didn't already exist I would have had to write something like it myself.