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Hi,
I am doing the same run on two different parallel machines on 4 CPU's each one build on xeon processor and another on 2 dual Opteron machine. All the values in the Free energy of the ion-electron system below, are the same except

V(xc)+E(xc) = XCENC

Free energy of the ion-electron system (eV)
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alpha Z PSCENC = 2219.11116875
Ewald energy TEWEN = -24693.41994369
-1/2 Hartree DENC = -6333.65344275
-V(xc)+E(xc) XCENC = 806.77569300
PAW double counting = 18439.13923259 -17825.34637919
entropy T*S EENTRO = 0.00000000
eigenvalues EBANDS = -609.51666535
atomic energy EATOM = 29088.32474472
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free energy TOTEN = 1091.41440808 eV

What could be the reason for this difference and what does the term V(xc), E(xc) and XCENC mean?

maybe the reason is the default optimization of xcgrad.o and xcspin.o in the makefiles, on some machines (compilers) the optimization level is too high and has to be decreased to -O0.
Please re-compile vasp on both machines with -O0 set explicitely for the compilation of these 2 files, and check if the results are the same then. (if they are, please increase the optimization step by step, up to the highest level which gives the same results).