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

No.

The spelling and grammar of "dirige" (the third-person singular present of dirigir) are identical in both dialects. However, there are significant differences in typical usage and pronunciation:

• Usage: In Brazil, "dirigir" is the standard, everyday verb used for operating a motor vehicle (car, bus, etc.). In Portugal, "conduzir" is the natural and standard verb for driving a vehicle. In Portugal, "dirigir" is typically reserved for the act of leading, managing, or directing something, such as a company, an orchestra, or a meeting.
• Pronunciation: In Brazilian Portuguese, the "di" syllable is palatalized, sounding like "dji" ([dʒi]). In Continental Portuguese, the "d" is dental, sounding much closer to the English "d" in "dog" ([di]).

Brazilian Portuguese Examples

1. Ele dirige muito bem. (He drives very well.)
2. Quem dirige o caminhão? (Who is driving the truck?)
3. Ela não sabe dirigir ainda. (She doesn't know how to drive yet.)
4. O diretor dirige a reunião. (The director directs/leads the meeting.)
5. Você dirige o carro com muita pressa. (You drive the car with a lot of haste.)

Continental Portuguese Examples

1. Ele conduz muito bem. (He drives very well.)
2. Quem conduz o camião? (Who is driving the truck?)
3. Ela não sabe conduzir ainda. (She doesn't know how to drive yet.)
4. O diretor dirige a reunião. (The director directs/leads the meeting.)
5. Tu conduzes o carro com muita pressa. (You drive the car with a lot of haste.)