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

No

While the spelling and the fundamental meaning of the word "acho" (the first-person singular present of the verb achar) are identical in both Brazilian and Continental Portuguese, there are significant differences in the grammar and typical usage of the word in a sentence.

1. Grammar (Syntax): In Brazil, it is common and natural to use direct object pronouns after the verb (e.g., "Acho ele..."). In Portugal, this is considered grammatately incorrect in standard speech; instead, clitic pronouns are attached to the verb (e.g., "Acho-o...").
2. Typical Usage (Context): The vocabulary surrounding the word "acho" varies. A Brazilian might use "legal" (cool) or "celular" (cell phone) in a sentence containing "acho," whereas a Portuguese person would more naturally use "simpático" (nice) or "telemóvel" (mobile phone).
3. Typical Usage (Articles): In Portugal, it is much more common to use definite articles before possessive pronouns (e.g., "a minha chave" vs. the Brazilian "minha chave").

Brazilian Portuguese Examples

1. Acho que vai chover. (I think it is going to rain.)
2. Acho que ele é legal. (I think he is cool.)
3. Acho que achei minha chave. (I think I found my key.)
4. Acho ele muito inteligente. (I find him very intelligent.)
5. Acho que você está certo. (I think you are right.)

Continental Portuguese Examples

1. Acho que vai chover. (I think it is going to rain.)
2. Acho que ele é simpático. (I think he is nice.)
3. Acho que encontrei a minha chave. (I think I found my key.)
4. Acho-o muito inteligente. (I find him very intelligent.)
5. Acho que tens razão. (I think you are right.)