Ammonium nitrate is generally pretty difficult to work with in the sense that it is very hard to get a sustained detonation without the proper setup and a little competence. While very popular in the mindshare of the public, it is quite a bit safer in that rank amateurs will have a hard time getting results out of it. TATP is much, much easier for an amateur to deploy successfully.
Unless you let the mixture sit around to long, then the slurry can become very unstable.AWB