SYSDBA

• Perform STARTUP and SHUTDOWN operations
• ALTER DATABASE: open, mount, back up, or change character set
• CREATE DATABASE
• CREATE SPFILE
• ARCHIVELOG and RECOVERY
• Includes the RESTRICTED SESSION privilege

Effectively, this system privilege allows a user to connect as user SYS.

SYSOPER

• Perform STARTUP and SHUTDOWN operations
• CREATE SPFILE
• ALTER DATABASE OPEN/MOUNT/BACKUP
• ARCHIVELOG and RECOVERY
• Includes the RESTRICTED SESSION privilege

This privilege allows a user to perform basic operational tasks, but without the ability to look at user data.