In this particular instance, I would agree that AA would be better. I'm a huge fan of Spirit, but their best deals are on point-to point service from Fort Lauderdale. Living in Florida, this is great for me but for people up north the difference is marginal and the service is non existant. It's flying public transport plain and simple. On connecting flights, their fares are not bad, but not that great of a deal. No Spirit airline flight is worth $343 dollars. $150-$200 for an international flight, yes its worth taking them.(Which i often get from Florida to DR) But for that price I just assume take AA
One more thing to consider is that there is usually a tight connection if you are arriving from their Latin American flights and connecting to points north. Terminal 4 is an absolute madhouse most of the day, and Immigration and Customs facilities, as well as TSA screening facilites, are woefully inadequate since because of Spirit, this terminal handles far more passengers than it was designed for. In the late afternoon, many Spirit Airlines flights from Latin America arrive within a few minutes of each other. (In addition to Air Jamaica and Avianca flights) Expect long lines both at US customs and then on security screening for your connecting flight.