Additional info from different servers.
Same value (1132495864) on 2016 (SP1) (KB3182545) - 13.0.4001.0 (X64), collation Latin1_General_CI_AS
Different values (AsChar=34400, AsNChar=1132495864) on Azure SQL Data Warehouse - 10.0.8506.1, collation SQL_Latin1_General_CP1_CI_AS
Different values (AsChar=34400, AsNChar=1132495864) on SQL Azure (RTM) - 12.0.2000.8, collation SQL_Latin1_General_CP1_CI_AS
Noticing that the collation was different, for giggles I then ran the following on SQL 2016 (SP1).
select checksum( cast('abc' collate SQL_Latin1_General_CP1_CI_AS as char(3) )) as [AsChar], checksum( cast('abc' collate SQL_Latin1_General_CP1_CI_AS as nchar(3))) as [AsNChar]
Behold, the figure were different!!! (AsChar=34400, AsNChar=1132495864)
So it appears to be a collation issue and not a change between the Earth and Cloud versions.
PS Thank you Grant for your initial response, that gave me the nugget I needed to work out what was happening.