How are Rolls-Royce engines different to others?
Yes, RR engines typically have 3 spools while GE and P&amp;W generally have 2.  There are several design tradeoffs.  Briefly:

3 spools are easier for the aerodynamic design. For example, compressor stall can happen when the front stages of the compressor are pumping more air than the back stages are able to accept.  On a 2 spool machine, the front and back stages are all on the same shaft going the same speed.  However, on a 3 spool machine, the front and back stages are on different shafts.  So one shaft can speed up or slow down to better match the stages.  To work around this issue, 2 spool machine usually need to have more variable geometry (such as variable stator vanes) than 3 spool machines.

2 spools are easier for the mechanical design.  Every spool needs to be supported by bearings.  More spools means more bearings.  Bearings have to be supported by frames and cases.  More bearings means more frames (or more complicated frames).  Every spool has critical speeds. So more rotors means more possible critical speed issues.  

There is not a clear winner.  2 spools are better for some things but 3 spools are better for the other.  Each company is going to tell you that theirs is "the best", but really they are about even overall.