Fullmetal Alchemist 2003>>>FMA Brotherhood.
The anime I watch typically has little to no fan service. That phrase can mean many things, but I generally dislike any fan service whatsoever.
Both series are great and worth watching.
Fullmetal Alchemist (2003) has better, more deliberate pacing for the first half and you get to know the brothers a lot better. Some of it is filler, but it's fairly well-written filler. It does its own thing for the second half, but it's still very compelling and it left a big emotional impact on me that wasn't there when I watched Brotherhood (although I was older by then, which may have contributed.) The original series also has significantly better music (not counting the openings, though Rewrite remains the king.)
Fullmetal Alchemist: Brotherhood (2009) is the better series overall and one of the greatest shonens of all time. The animation is consistently fantastic in a way only Hunter x Hunter can match, and the show juggles a massive cast of main and secondary characters with aplomb. By the time the series reaches its endgame, shit goes down in the most satisfying way possible.