Oracle GoldenGate(OGG) and Oracle Data Integrator(ODI) are two kinds of product. Oracle GoldenGate is non-intrusive real-time CDC whereas Oracle Data Integrator is an ETL tool (in Oracle’s term, it is E-LT tool).
Oracle GoldenGate differentiates itself by the characteristics of being real-time and non-intrusive, heterogeneity and flexibility whereas ODI by performance, simplicity and cost-saving.
These 2 products stands for different kinds of needs. If you want to replicate data with a minimum set of transformation, Oracle Golden Gate is good for you. But if you want to make lots of transformations (eg. loading a data warehouse, OLTP reporting, merging different systems), Oracle Data Integrator should be your first choice.
OGG works with log shipping method (which only works with databases that support log shipping), but ODI works with JDBC (java database connection) any type of database. JDBC driver is the only thing that you need to connect to a datastore.
OGG is a replication tool, but ODI is an E-LT or ETL tool. They stand in different scopes.
Both are good products. Really depends on what you want to do. If you are looking to run a product that can run something like a brokerage project, with little configuration, then you should go with GoldenGate. If you are looking to run daily operations for Integration then you should use ODI.
To be clear ODI can also do real time integration, but in my opinion GoldenGate does it the best.