This is a bit vague answer as I don't have any good references at hand beyond "having read books" a while back. But I will give a short answer to a wide topic.
The roman legions was well trained and had discipline, they were paid professionals with weathered veterans teaching the younger ones. Comparing that to the other general armies of the time which were often ill trained, not as well equipped and in many cases fought against their will it is not hard to imagine the outcome of battle.
Other armies were much more so individualists, where the roman legion was a unit of well composed hardened soldiers. Also remember, back then the premises of battle was different, much more chaotic and not as good "widespread" communication. If one army's front line would be breached it could cause their whole army to collapse, causing panic and turn in to a mass flight. With the strong moral in the roman legions (and the hard punishments upon failing the commander) (https://en.wikipedia.org/wiki/Decimation_(Roman_army)) this made the roman legions a successful army for a long time.
(another link discussing a bit of what I've said http://www.ancientmilitary.com/roman-military.htm)