I forgot where, but I've seen Fullmetal Alchemist described as a "shounen fighting manga" a few times. Personally, I don't think that's an accurate description.
While the premise for Fullmetal Alchemist is not too unusual, fighting is not its main objective. It's not about "I'm going to be the best ____ ever!". After all, as Arakawa says, Ed starts out at level 100. Whenever he and Al say they've progressed, it's not in fighting ability, but emotionally and intellectually. In Chapter 16, when Ed and Al travel to meet Izumi, Ed says it's because they "want to get stronger." Winry thinks he means they want to be stronger at fighting, but Ed retorts that it's not "something so simple," and they want to become stronger on the inside.
Even when there are battles, it's depicted in a realistic manner. In a lot of other "shounen fighting manga" that I've read, even the really good ones like One Piece, it frustrates me how the characters just talk and talk and talk, boasting and boasting, and then dish out a few moves. It makes me wonder, if they're so badass, why don't they just GET TO IT?
In Fullmetal Alchemist, the characters don't hesitate before launching into battle. They can begin suddenly and spontaneously, and many times the characters even interrupt each other in the middle of a sentence to throw a punch. Many times there's no clear victor, and fights can be broken off or postponed for any number of reasons.
And even then, Fullmetal Alchemist focuses on plot more than action. The most fight-heavy part of the manga so far is Volume 7. In other volumes, there is maybe one or two fights, and sometimes they're only brief skirmishes. The only fight that is actually prepared for tournament-style is the Ed VS Roy fight in a short humorous Gaiden.
There are no power levels or power-ups. There are no attack names. While the characters might use alchemy in battle, it's not in an organized manner, and in fact most of the time Ed and Al's opponents don't use alchemy. Ed's fighting style doesn't lend itself to attack names either (how weird would it be for him to say "Automail Blade Slash!" or "Automail Leg Kick!"?). There's no time to explain attacks, or even a need to, because it's all pretty self-explanatory.
So I guess my point is, while Fullmetal Alchemist may have fights, it's not a fighting manga. I'd describe it as just a shounen adventure manga. Agree? Disagree?
*goes to take a nap before the next class*