What file systems does Apple use in iPhones?
According to iOS Forensic Analysis, the main filesystem is HFSX.

HSFX
All Apple mobile devices use HFSX as the file system. HFSX is a variation of HFS+ with one major difference. HFSX is case sensitive.

HFSX is reported by Apple as Mac OS Extended (Journaled, Case-Sensitive).
There are two main partitions of HFSX: the OS and the user data. Prior to these partitions is the usual MBR partition (around 100 MB).

SSHing into my jailbroken iOS 6 device seems to support this, since I can create case-sensitive directories. Creating the following directories was no problem:
$ mkdir test
$ mkdir Test
$ mkdir TEST