FullMetal Alchemist is the first version of FMA. It was made during the first stages of the manga, so the plot is different. Arakawa, the creator of FMA, asked them to do this because the manga wasn't far enough and therefore, there was basically no storyline. So, the animators came up with there own story.
FullMetal Alchemist: Brotherhood came out a few months ago, because the manga is now far enough for a real anime. Brotherhood starts off after episode 3 of the regular version, so that the production company could save time and money. The new version follows the story from the book; A totally new plot, with a totally new conflict.
I suggest you watch FullMetal Alchemist first, because it goes more into detail with the character's lives. If you start from Brotherhood, you'll miss the first 3 episodes, and it will become very confusing.
In my opinion the 1st is one of the best anime i've ever seen hilarious but also serious and intense. And it has the coolest characters…