The Broken Cross has Pagan roots, being the inverse of the Pythagorean symbol for life and Teutonic rune of death, and is vogue with Wiccans and Satanists. It can represent the antithesis of all that Christianity stands for.
Some see breaking a cross as a way to protest against Christianity. An example of this has been witnessed in recent years in Armenia (see Khachkar Cross).
The Broken Cross has been called a Neronic Cross or Nero's Cross in recognition of Nero's attempt to suppress the rise of Christianity (see St. Peter's Cross). It seems illogical to connect a symbol of Christianity to people opposed to the religion, albeit inverted and broken, but labelling this as Nero's Cross has found its way into reference books and no doubt will continue to mean different things to different people. (See The Meaning of the Christian Cross)
Enclosed in a circle, the Broken Cross has been the emblem of the Campaign for Nuclear Disarmament since 1958 and the symbol has become synonymous with 'Peace'. Some dismiss the CND as somewhat anti-establishment or anarchist, but it's well worth reading what they have to say before passing judgement. (See for example, the Christian Campaign for Nuclear Disarmament http://ccnd.gn.apc.org/.) It's easy to understand why countries such as Japan are slow at adopting Christianity when the only country to have used an atomic weapon is seen as a Christian nation.
The designer of the CND logo, Gerald Holtom, choose something that would be easily recognisable, like the radioactivity hazard symbol, and circular, so it would be suitable for a badge. It was not his intention to use a Broken Cross per se, but simply incorporated the Semaphore positions of 'N' and 'D', an acronym for Nuclear Disarmament.
(For other peace symbols, see Pax Cross and Dove Cross).
Finally, the Broken Cross could be seen as simply an upright Stipe supported by two lower beams. Whilst most people envisage the cross used to crucify Jesus was the Latin Cross or Tau Cross, some (for example, Jehovah's Witnesses) believe Jesus was actually crucified on just an upright wooden post; Crux Simplex.
Whatever the design of the cruciform, it was quite possibly a stipe that Jesus was fastened to for scourging prior to his Crucifixion. The stick used to beat Jesus is featured on the Arms of Christ page. This armament is very different to that mentioned above - the armaments of man built for destruction.