Native speaker of a target language or fluent speaker of a target language?

Each has its pros and cons. Why not both? Know more won't hurt!

Native speakers, since they are so familiar with their own languages, won't care if the sentences are grammatically correct as long as others understand them. Fluent speakers who has been to intensive courses can be more accurate than native speakers since they really "learn" and remember all those grammar rules. They won't learn much slangs at those courses.

Fluent speakers may not know the cultures as well as native speakers. Even if a Westerner who has been through lots of courses and has taken lots of Chinese examinations, this doesn't mean he knows Chinese cultures. He won't understand the importance of "filial piety" in Asian society as well as Chinese.

If the native speakers of a language are not well-educated, the unintentional use of slangs and colloquial words would be common in their speech. If the fluent speaker has 'learnt' that language in a school/college, it would be free of slangs and grammatically correct.

The patience of the person you are speaking to is more important than either of your criteria.