SQL to MongoDB for full text search

I have a (big) 50GB SQL-Database with ca. 500.000 entries.

The entries have a large text field that I want to search. So far I’ve been using MariaDB and have a full text index there. The search works, but despite the index, it takes a long time depending on the search term. (1sek to 15sek)

A friend recommended MongoDB to me. Now I have created one as a test and imported my data. I have also already placed a text index on the field. Times aren’t that much better either.

Hence the questions:
a) Objectively, is MongoDB better for full-text search in large databases?
b) What do I have to adjust to make the search run faster/better.
(I just use the community version, not atlas)

I look for normal words in the texts: “computer”, but also for special phrases “Euro 5”, which must also appear in the text with the space.