In which case would the use of informal syntax be more appropriate than a formal syntax?

That would actually depend on the context and the situation. Formal syntax is obviously appropriate for formal situations, such as meetings, lectures, memorials, etc. (in spoken form), or research papers, analyses, non-fiction (in written form). 
On the other hand, informal syntax would be appropriate for informal situations, such as hanging out with friends and family (in spoken form), or fiction, dialogues, etc. (in written form).