What could cause GE and Rolls-Royce turbofan engines to sound different?
The GE90 engines have a higher bypass ratio than the RR Trent.  

The majority of engine noise, especially the "ripping, howling, typical jet noise" comes from the engine core.  

The higher the bypass ratio, the less air passing through the core for any given thrust and the more cold air meets the core exhaust at the back reducing the shear

Jet engines with no bypass ratio and deep intakes produce a wonderful sound