I'm not exactly sure what you mean when you say "both Axis and Allied powers greatly respected each other (the men fighting anyway)". Did you mean to refer to the First World War instead? I'm assuming that you did.

But as to your actual question, it's vital to understand how war was seen in Europe at the beginning of the 20th century, as well as how the relationships between European countries were seen. Despite the First World War taking place in the second decade of the 20th century, the mindsets of many monarchs, generals and officers were still firmly stuck in the 19th century way of seeing things; honour was valued above all else, and while you may be at war with a nation, it doesn't mean you hate them or even want to kill them; in other words, it was business, not personal. Add to this the fact that many of the monarchs of European powers were actually related to each other. For example, Kaiser Wilhelm II of Germany was cousin's with Tsar Nicholas II of Russia, who was cousin's with King George V of Britain. Even as Germany and Russia geared up for war with one another, the Kaiser and the Tsar sent each other personal letters of warmth and consideration, and referred to each other's nicknames.

So for the European powers - even though they were engaged in massive, bloody wars with each other, there wasn't really a feeling of deep-seated hatred or anger, it was more just like... business... really. As nasty and destructive as wars were, it was still a socially acceptable and even noble thing to meet each other face-to-face in battle and fight with honour and bravery. This had gone on for centuries and it was basically the norm; there's a breakdown in negotiations and diplomacy, you meet your opponent of a field of battle, and the best side wins, and then the negotiations resume and all is back to normal. There's no reason to deeply and personally hate the men you fight; sure they are your opponents, but they are loyally and dutifully serving their king just as you are, so it's nothing personal.

But with the swift and brutal ends of the three major European monarchies at the end of the war (Germany, Austria-Hungary and Russia), in their place was not a king or emperor from a noble bloodline, allowed to rule by the grace of God - things that all Europeans respected - but instead rabble-rousing populists; politicians and writers and lawyers intent on stirring up the fears of the people and lighting the fuse of violent nationalism. These 'leaders' didn't come from long lines of royal ancestry, but from the universities and the streets. They demanded not loyalty to a king or an emperor, but to the state, a very vague concept that is hard to put a clear definition to.

Kaiser Wilhelm II (or "Willy" as he called himself in his letters to his cousin "Nicky", the Tsar of Russia) was gone, as was his cousin Tsar Nicholas. In their spots were Adolf Hitler and Joseph Stalin, men who came from nothing and cared nothing for the old traditions or the old values of honour and mutual respect. All they lived for was the state, and seeing their own state reign supreme at the cost of everybody else. This was distinctly not how the old powers of Europe had thought. While they had certainly wanted to be victorious in their imperial endeavours, they certainly didn't want to commit genocide against ethnic groups or wipe out entire corners of the continent. But things were different now. There was no room left for honour or mutual respect or mercy; the state cared nothing for these outdated concepts left over from a more enlightened time. Hitler and Stalin riled up their citizens not to fight against other Europeans (as had been the idea in the First World War) but to fight against inferior races, weak races, races that had no place in Europe. Both in Europe and in the Pacific, this war was to be much more deeply driven by ideas of race and racial superiority (Aryans vs Jews, Aryans vs Slavs, Caucasians vs Asians, etc). It's much easier to hate someone you conceive as being racially different (and therefore inferior) to you than it is to hate just another European serving a different king or emperor.

Not only was the political leadership and race driving factors in the more vicious nature of the Second War World, but so to was the sheer volume and severity of the war crimes committed against civilians; the rampages of the Germans in Russia, and the Russians' retaliation when they marched on Berlin, as well as the Japaneses' Rape of Nanking against the Chinese. It's one thing to kill hundreds of thousands of armed men who are also trying to kill you; but to know that your enemies have raped, tortured and massacred your friends, your family and your neighbours... that inspires a hatred frightening to imagine. Granted, the First World War saw war crimes committed too (the Rape of Belgium being the first to come to mind) but nowhere near the scale the Second World War would see. The cycle of war crimes followed by retaliation was incredibly brutal for all sides involved.

tl;dr: the change in the nature of the wars can be summarised to several key factors such as the disillusionment with 19th century romantic ideals, the drastic and violent changes in political leadership, the increased focus on nationalism and racism, and the shocking and unprecedented level of war crimes committed.