How important is pronunciation?

The trend these days is to replace the word "good" with "appropriate", which is socially context specific. Both "grammar" and "pronunciation" can be considered co-aspects of an idiolect, with "standard language" as a socially neutral form. Use of standard language can alienate speakers from their social peers but is a safe option for formal contexts. In such contexts, standard grammar is probably considered more important than standard pronunciation because conformity in grammar tends to be the primary indicator of communicative ability and hence of the prospect of mutual concurrence. In general however what tends to happen as a successful meeting proceeds is that convergence operates (especially in pronunciation) involving both parties finding a mutually satisfactory style which may depart from "standard", or even each others default idiolect.

Six of one...

Good grammar is more important.

The latter would be like arguing about the better pronunciation of the word "tomato."

Depends on what you're speaking. I speak English,Creole,Urdu(1st language),Arabic, and some Pashto. Must be very careful when speaking Urdu,Arabic, and Pashto because different tones and syllables give words different meanings.