I'm using some tables like pg_stat_user_tables and to optimize pg_stat_user_indexes our indexes and I found that this table it's different between the writer and reader.
Someone knows why this happens? And which table we can trust for tunning?
This is expected. Statistics that are 'usage' related are specific to the instance/server. Only stats like pg_stats which has things like ndistinct, most common values/frequencies, histogram, etc --- basically what is the "shape/size" of the data stored in tables (and functional indexes, and multi-variate statistics objects that get created) would be the same between primary & reader.