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

Yes

The word "delicioso" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazil, the vowels are generally more open and clearly articulated. In Portugal, unstressed vowels undergo significant reduction; for instance, the "e" and "i" sounds are often shortened or nearly silent, resulting in a more "closed" phonetic structure.

Brazilian Portuguese usage

1. Este bolo está delicioso! (This cake is delicious!)
2. Que cheiro delicioso tem esse jardim. (What a delicious/lovely scent this garden has.)
3. O jantar de ontem estava delicioso. (Yesterday's dinner was delicious.)
4. Eu fiz um suco delicioso para você. (I made a delicious juice for you.)
5. O dia está delicioso para passear. (The day is delicious/lovely for a walk.)

Continental Portuguese usage

1. Este bolo está uma delícia! (This cake is a delight/delicious!)
2. Que aroma tão bom tem este jardim. (What a very good scent this garden has.)
3. O jantar de ontem estava ótimo. (Yesterday's dinner was great.)
4. Eu fiz um sumo delicioso para ti. (I made a delicious juice for you.)
5. O dia está uma maravilha para passear. (The day is wonderful for a walk.)