For the reasons mentioned by rngadam, war crimes do tend to get committed in most conflicts.
The crimes are committed during the conflict; we don’t know who the winner is until after the conflict. For that reason, if for no other, it would be irrational to assume that all crimes, or the bulk of crimes, are committed by the losing side.
As against that, there’s no reason to assume that crimes will be proportionately distributed among all the combatant armies, so to speak. If nothing else, members of the more powerful, better-equipped, better-led army (which will, of course, tend to be the winner) are less likely to find themselves in the kind of desparate situations which can lead to the commission of war crimes. Other factors can, of course, lead to war crimes – e.g. a criminal policy by a combatant state or by the leadership of a combatant army – but confusion, danger, desparation and panic must, intuitively, form a singificant part of it.
Where crimes are committed, my guess would be that offenders on the winning side are, broadly speaking, less likely to be prosecuted and, if prosecuted, are likely to be punished less severely, than offenders on the losing side. Just a hunch, nuthin’ more. Sorry, folks, no cite. For an isolated comparison which may not be representative, consider the treatment afforded to Lt Calley, convicted in connection with the My Lai massacre of Vietnamese villagers (sentenced to life, sentence progressively reduced to twenty and then ten years, released on bond, then paroled after serving, all told, three-and-a-half years) as against that afforded to Adolf Eierman, a German civilian convicted of instigating the beating to death of a wounded American airman (hanged).
Brutus is right to say that the US Code of Military Justice proscribes war crimes, and that US service personnel can be and are prosecuted under that Code. However under that system suspicion will always remain (to put it no higher) that, where the victors are dispensing justice to their own friends, supporters and agents, impartial justice of the kind we consider essential to the rule of law is not always to be expected.