Confederate Generals did seek employment in Egypt, Brazil and Mexico, if I recall.
The main advantage would be actual battle experience (and in most cases, at least semi-formal military training) and, for non-American powers, the fact that they were not European, e.g. they weren't here to spy out your fortifications, and Britain/France/Spain wouldn't complain about their presence here. This is especially important for the modernizing states in the Middle East. For American states, the important thing was that they weren't loyal to the USA either, so the same reasoning applies.
Of course, Germans and French advisors were more highly-valued but if the two happened to be engaged in major wars and had to recall their officers, it's not inconceivable that the market for Confederate leaders would have been much higher.