What are the arguments in favor of using ELT process over ETL? I realized that my company uses an ELT (extract-load-transform) process instead of using an ETL (extract-transform-load) process.
What are the differences in the two approaches and in which situations would one be "better" than the other? It would be great if you could provide some examples.
lots of Discussions about ETL vs ELT out there.

The main difference between ETL vs ELT is where the Processing happens
ETL processing of data happens in the ETL tool (usually record-at-a-time and in memory)
ELT processing of data happens in the database engine

Data is same and end results of data can be achieved in both methods.

it very much depends on you and your environment
If you have a strong Database engine and good hardware and you can do heavy processing on it, ELT is good for you, 
If you have a busy datawarehouse engine and you need to free it from processing go for ETL.

notice that having an ETL tool gives you both the options, like ETL(T), you can do the Transformation in the ETL tool and you can do transformation in the Database engine as well

but ELT you only have the option of transformation in the database engine, but you should know that Databases are better at set based operations than record-at-a-time ETL tools.

similar question asked on SO but supporting ETL and also
a nice Article comparing ETL vs ELT, but favoring ELT