In WWI you have stories like the Christmas Truce of 1914 and other anecdotes where soldiers had a mutual sympathy for each other. Dan Carlin's podcast has an account where two armies have their trenches flooded and they both come out so as not to drown and no one shoots at each other.
Yet in WWII there are a lot of stories about killing German POWs and civilians and few about non-aggression or kindness towards the enemy. The TX State dissertation that was posted not too long ago here had a story about an American shooting a German boy for Sieg Heiling, and another where an American chased a naked German prisoner with his bayonet for sport until finally killing him.
Did WWII have these same acts of "live and let live" but they're just overshadowed by other acts of cruelty? Or was that attitude largely gone by WWII and if so, why?
^ this series of answers should be pertinent.
In WWI you have stories like the Christmas Truce of 1914 and other anecdotes where soldiers had a mutual sympathy for each other. Dan Carlin's podcast has an account where two armies have their trenches flooded and they both come out so as not to drown and no one shoots at each other
I would hesitate to over play the Christmas Truce; it was primarily a happening in the British sector, which was very small at the time, although some Belgian and French units may have partaken. More often than not it was to do with nothing going on in the trenches on either side. Rather unsurprisingly, the soldiers on both sides hailed from European, Christian traditions that celebrated Christmas. There are some cases of fraternization, or more commonly an agreement to recover wounded/not fire on either side, though there are also plenty of accounts of truce offers by either side being met with bullets.
Taking prisoners was common in WWI and WWII, but in both wars, the unspoken 'politics of surrender' (as Canadian historian Tim Cook has referred to them as) held sway. Recent combat, heavy losses, foul play by those surrendering, and the feelings of the soldiers themselves, governed how prisoners would be treated upon surrendering. In this respect, WWI and WWII are not that much different, through in WWII of course there were armies that in certain cases (German Army in the East, Red Army in the East, Japanese and Allied forces frequently in the Pacific) would not necessarily accept a surrender, or would brutally mistreat (and in the German case in 1941, starve en masse) POWs.
It's also worth noting that here, treatment of POWs in WWI had an affect, specifically with the Geneva Conventions. These were the result of often brutal treatment of POWs in WWI: Romanian and Russian POWs were very poorly treated in German hands, and this seems to have extended to Italians in Austro-Hungarian hands. The French, though not the British, drifted towards reprisals against German POWs (often with reduced conditions and rations, working at the frontline) but this was fairly tightly policed by the civilian governments, and ultimately discontinued. Moreover, it was a response to reprisals against more numerous Allied prisoners in Germany, where by 1917 'Reprisal Camps' were set up, and in 1918 mass use of Allied POWs, in appalling conditions behind the frontline, was utilized.
Excellent sources for the WWI side of things would be Tim Cook's article Politics of Surrender, focusing on Canadian troops. Niall Ferguson also wrote an article about surrender and prisoners in the age of Total War, and Heather Jones and Alan Kramer have both written books on violence against POWs in WWI. Isabel Hull's A Scrap of Paper is excellent for International Law in relation to WWI, and goes into detail about reprisals and treatment of POWs.
TL;DR: Live-and-let-Live was present in both wars, but should not be over-emphasized. Although WWII was on the whole more brutal for POWs, this also had to do with different policies held by some Powers engaged in that war.