I'd be interested in getting the opinion from users of GAMS and AMPL on what the strength and weaknesses of each these languages are.
In terms of functionality they are pretty much the same allowing to express most types of optimization problems. Personally, I prefer AMPL because it has intuitive and expressive syntax and it is very well documented in the book. Another important advantage of AMPL is that despite the fact that it is commercial you can avoid the vendor lock-in because there is an open source alternative - GNU MathProg. GAMS on the other hand used to have a more advanced IDE than those that existed for AMPL although it changed with the introduction of the new AMPL IDE.
You can find an example of the same transportation problem from George Dantzig formulated in AMPL and GAMS in their Wikipedia articles: AMPL and GAMS.