Are they the same?
No, they are different in meaning.
According to him - in his opinion
According to the latest reports...
Due to - because of
The aircraft couldn`t take off due to the fog.
To be due - should come/must come/supposed to come or arrive/one`s obligation to do smth.
He was due to appear in court last Friday but didn`t show up [ He should have come.../He had to appear in court..]