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

Yes

The spelling, meaning, and grammatical classification of "hospital" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The "l" at the end of the word is typically vocalized, sounding like a "u" (ospi-táu). The vowels are generally more open and the rhythm is more melodic.
• Continental Portuguese: The "l" is a "dark L" (a velarized lateral consonant), meaning the tongue touches the roof of the mouth more distinctly. The vowels are much more closed and reduced.

Brazilian Portuguese Examples

1. Eu vou ao hospital agora. (I am going to the hospital now.)
2. O hospital é muito grande. (The hospital is very big.)
3. Ele está no hospital fazendo exames. (He is in the hospital doing tests.)
4. Tem um hospital perto da minha casa. (There is a hospital near my house.)
5. Você precisa ir ao hospital urgente. (You need to go to the hospital urgently.)

Continental Portuguese Examples

1. Vou ao hospital agora. (I am going to the hospital now.)
2. O hospital é muito grande. (The hospital is very big.)
3. Ele está internado no hospital para fazer análises. (He is admitted to the hospital to do tests.)
4. Há um hospital perto de casa. (There is a hospital near home.)
5. É necessário ir ao hospital com urgência. (It is necessary to go to the hospital with urgency.)