Postgres is better than mysql in many ways. You can read these posts about migration rails app from mysql to postgres. Though mysql is more popular than postgres, but instagram is using postgres maybe due to these reasons. I feel postgres is much more mature and robust than mysql. Whereas mysql is more easy and simple to use.
Migrating MySQL to PostgreSQL in Rails « m i n d l e v
Converting Rails application data from MySQL to PostgreSQL
For data migration, a handy little script: Rake task to transfer a Rails database, say from MySQL to Postgres and back again