Postgres index size calculation
There is no general way to answer this (other than try it on your test server and see).  GIN supports many different operators, like tsvector or trigrams, and they have different characteristics.  In newer versions, GIN indexes use compression which can be pretty impressive when the same key value shows up over and over again.  But that level of compression depends on the ordering of the rows.

For example, if I index a single text column with a lot of duplicate values (~50 million rows, with ~1.5 million distinct values, using the btree_gin extension for the GIN), I get 2010 MB for the b-tree index and 435 MB for the GIN index.  So no, the GIN is not always bigger.  But in general (i.e. other than with btree_gin) you don't index the same types of data with GIN as you do with b-tree, so a direct comparison of sizes does not make much sense.