After setting up streaming replication, is it possible to check whether the slave has the same data as the master?
Yes. There are quite a few ways to check the sync status between master and standby. Which version of PostgreSQL are you using by the way ?
Generally, you can easily build some scripts and schedule them in cron to check the status. You can use functions or catalog views to monitor the status, this depends on the version of PG you are using.
You can also use tools like "repmgr" to monitor and manage replication. I am not 100% sure how good or efficient it is.