Despite having very different goals, both manga have some similarities. Such as the physical similarities between Ed and Allen as well as the running theme of Good vs Evil. However, D.Gray-man has a "religious" aspect in the manga, while FMA was based upon science and alchemy.
The Main Character (Allen/Ed) feel the same about their comrades, act similar and the Plot is almost the same - Searching for something very important.
Also, the humour is very similar for example when Kanda calls Allen a beansprout and the people in FMA call Ed Shortie and both react a bit... unfriendly ^-^
Both of these manga are have a lot of humor in them, but the central plot is more on the sad side. The main characters of both FMA and DGM have some kind of issue with one of their arms, and both series involve rather supernatural things. Each also has a plethora of characters, including "the annoying (but awesome) higher up" and "the 'evil' teacher."
Overall, both DGM and FMA are great series, and should definitely be on everyone's Must Read List.
In many ways Allen Walker, the main character of D.Gray-Man, and Edward Elric, one of the main characters of Fullmetal Alchemist are similar. To the way they try to protect everyone around them even when it means sacrificing themselves, having a weapon for a arm. Both series have similar enemies as well. The antagonist(s) of each series has a grudge against mankind and they believe its their duty to destroy it.
Atypical battle shounen, more found in the drama and the characters than in the fights. Both deals with religious and dark themes, mostly concerned about resurrection. The main character is similar in personality and a bit in looks, and both have a special arm that they use to fight.
"Dark shounen"s.. DGM has some 'dark' qualities that FMA had.. Both have some sad stories / dramas.. Allen (DGM main protagonist) is an intermediate (has and doesn't have some characteristics) of Ed and Al (FMA main protagonists)..
The main characters of both mangas are very similar in physical appearance.Both have similar themes but D.Gray-man is more about religion and stuff and Fullmetal alchemist is more about alchemy and equivalent exchange.
Both series are Battle Shounen-series in a steampunk-like-setting. Fullmetal Alchemist has alchemy and Homunculi, while their are other artificial created beings in D.Gray-man, called Akuma. Both, the Homunculi and The Noah to a wider extent, portray the deadly sins.
The protagonists of both series work for an organisation, the state in FMA and the order in DGM, which hides some secrets. They have similar temperament and care about lives, but they are still very different in their core personalities. Both of them have a mechanical arm.