Bah, I was too slow at editing the previous post to fix a grammar mistake I had in it, and to append the follow message.
I don't think anatomy helps you very much, but physiology can when it comes to remembering what kind of signs and symtoms are associated with certain conditions, but a lot of EMT programs seem to do just fine either doing it cook book style or give you an analogy that doesn't quite hit in on the nail, but is understandable and easy for student to memorize. Knowing things like thorough A&P, medical terminology, pharmacology, pathyology will only make you marginally smarter within the scope of an EMT-Basic compare to others (it still won't help you execute your skills, but you'll get to know those like the back of your hand anyhow), however, if you plan on moving up within the medical field, I believe it will be necessary to know, and minus well get those out of the way, and be marginally better anyhow.
I took First Responder first. I personally feel that I could've done without in EMT since you will be required to go over it again anyhow. Sure you'll be better prepared for the lectures and skills the second time around, but if you can do it once, well, I personally see it as a waste.
Overall, learning is fun. It's cool to go above and beyond, talk pro, and be a boss. It looks like a lot of people would have loved to spend more time in school to go over things much more thoroughly.