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Core wire in musical strings is the inner most section of a wound string. Most core wires are hexagonal in shape versus round to help lock the wrap or cover (the outer part) of the wire in place thus preventing unraveling. Classical guitar strings uses a nylon filament core.
Different string makers have different dimensions of core wire, which does make a difference in sound. 
Coated strings are nothing more then a prevention of string deterioration from hand sweat etc., promoting extended string life. I believe string life would be extended by just wiping strings after playing time. Thus the same outcome.
No matter what kind of strings are used sooner or later they flatten where the string meets the fret (where the rubber meets the road). Frets will flatten the string leading to dead sound and difficulty in tuning.
Addendum 5/1/2011:
Many times owners receive setup services for a tremolo guitar (e.g., Floyd Rose, Kahler system, or Bigsby) and are not satisfied in that the instrument does not stay in tune despite strobe intonation, bridge work, and etc.
Guitar strings play a role in whether a tremolo system will return strings to tune whether or not a tremolo is used. The use of extra light or light strings that have a small core shows the weakness of a guitar string. That is, light strings with a weak core are open to constant tuning issues and early wear.