If I understand your question, I define high level language as using large vocabulary and sometimes complex grammar.
The advantage of using such language is that you an be more descriptive and convey nuances of meaning. The disadvantage is that people who speak the language as a second or foreign language user may not know your vocabulary and the grammar may confuse them.
Whenever one communicates with others, is it good to understand the audience and use language suitable for them.
I wonder if you are pointing to diglossia- speech communities where a low braw and a high braw variety are used side by side for different purposes. The high level language, using your wording, is used for official purposes, whereas the low braw variety is used within the inner group among friends and family members. Talking about disadvantages, you could say that the high level language viewed by the groups favoring the low level language is cold and cumbersome. In other words, they may not comfortable with it since such varieties often come from another culture ( e.g., considering the situation in India). These high level languages carry an idiosyncratic cultural identity which prevents the locals from enjoying the intimacy emanated by the low level language.
Hello, Rasha, judging from your backgroud I guess you are refering to high level programming language, I have no expertise in this aspect, nevertheless my reminder may help others who are specialize in computer languages.