Is UF allowed everywhere NM is allowed?
Multiconductor UF can go wherever NM goes...

While single-conductor UF is a thing for certain applications, the UF one sees in residential work is almost universally the multiconductor version, and that is permitted to be used anywhere NM can be used by NEC 340.10 point 4:


  (4) Installed as nonmetallic-sheathed cable. Where so installed, the installation and conductor requirements shall
  comply with Parts II and III of Article 334 and shall be of
  the multiconductor type.


However, UF isn't available in all the configurations NM is

According to Encore Wire's specsheet for NM-B, they make NM in /2 in 14 through 6AWG, /3 in 14 through 2AWG, /4 in 14 through 10AWG, and /2/2 in 14 and 12AWG.  If you look at their specsheet for UF though, there is no such thing as /3 UF fatter than 6AWG (you're expected to use a different direct bury cable type, such as URD or MHF, for applications upwards of 50A), nor are there any /2/2 or /4 configurations available (you're expected to use conduit if you need more than 3 wires + ground).