FAA Aircraft Dispatcher license: Do you recommend working regional OR charter?

A regional might get you more experience dealing with ATC and a busy flight schedule. A charter airline would probably have fewer flights but you could be more involved in building each trip by hand and dealing with more issues for the flight. I would say the most important thing is to get a job with a decent company where you will get good experience, whether it's regional or charter. Personal preference, if you have a choice I would go with the regional airline because they probably have better flight benefits.