Modulo-2 Addition using 1's and 0's binary data is equivalent to Multiplication using -1's and +1's binary data as long as we remain consistent in mapping 0's to +1's and 1's to -1's as clearly illustrated in the Truth Table above.
For circuit implementation, Modulo-2 addition is preferred since Exclusive-OR gates are much cheaper than Multiplication circuits.
For modeling purposes, the Multiplication Method is usually easier to formulate and understand than the Mod-2 approach.
