If I am understanding your experience correctly the colloquial wisdom here is to use GIN on static data and GIST on dynamic data.

In choosing which index type to use, GiST or GIN, consider these performance differences:

GIN index lookups are about three times faster than GiST

GIN indexes take about three times longer to build than GiST

GIN indexes are moderately slower to update than GiST indexes, but about 10 times slower if fast-update support was disabled (see Section 54.3.1 for details)

GIN indexes are two-to-three times larger than GiST indexes

As a rule of thumb, GIN indexes are best for static data because lookups are faster. For dynamic data, GiST indexes are faster to update. Specifically, GiST indexes are very good for dynamic data and fast if the number of unique words (lexemes) is under 100,000, while GIN indexes will handle 100,000+ lexemes better but are slower to update.

https://www.postgresql.org/docs/9.1/textsearch-indexes.html