Although MongoDB provides a lot of search functionalities, yet there are certain features which it does not support like:
1. There is no search based on synonyms
2. There is no support of using your custom stemmers and custom stop words list
3. You can only define one $text index for the entire collection
4. You cannot use hint() with $text
Elasticsearch, in my opinion, is much more advanced and meets most of the search requirements compared to MongoDB.
Regarding performance, according to the official MongoDB documentation :
1. "text indexes can be large. They contain one index entry for each unique post-stemmed word in each indexed field for each document inserted."
2. Insertion throughput is impacted when we create a $text index
3. Phrase searches are slower compared to token based search
Reference:
https://docs.mongodb.com/manual/core/index-text/#storage-requirements-and-performance-costs