I have the first edition of Strogatz' book. It's fairly accessible to students who have taken calculus and been exposed to ODEs, and can be worked through in about a semester. Great for a 200 or 300 level course.
Wiggins is a much more advanced, and much more thorough, book. It's appropriate for 400 level at a minimum, and probably more accessible to graduate students. I wouldn't even attempt it without having taken ODEs and Linear Algebra, and probably some real analysis or PDEs or another high level course just for exposure to mathematical rigor (and I might be leaving out other prereqs; I can't presently locate my copy of the book.) It's tremendously well presented for a book at that level, and could be enough material for a three-quarter or two-semester sequence. It's advanced enough that someone working on a related Masters or Doctoral thesis would likely refer to it regularly.
