Is the word dragão the same in Brazilian and European Portuguese?

Yes

The spelling, meaning, and grammatical category of "dragão" are identical in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, vowels tend to be more open and the rhythm is more melodic. In Continental Portuguese, vowels (especially in unstressed syllables) are more closed or even reduced, leading to a more "clipped" or staccato cadence.

Brazilian Portuguese Examples

1. O dragão soltou fogo pela boca. (The dragon breathed fire from its mouth.)
2. Eu vi um dragão voando pelo céu. (I saw a dragon flying through the sky.)
3. A criança desenhou um dragão bem grande. (The child drew a very big dragon.)
4. O dragão está assustando todo mundo. (The dragon is scaring everyone.)
5. O dragão é o personagem favorito dele. (The dragon is his favorite character.)

Continental Portuguese Examples

1. O dragão cuspiu fogo pela boca. (The dragon spat fire from its mouth.)
2. Eu vi um dragão a voar pelo céu. (I saw a dragon flying through the sky.)
3. A criança desenhou um dragão muito grande. (The child drew a very big dragon.)
4. O dragão está a assustar toda a gente. (The dragon is scaring everyone.)
5. O dragão é a personagem favorita dele. (The dragon is his favorite character.)