Very good question. I imagine people from different generations and in different parts of the world would give quite opposing answers. The answers people give will also be powerful indicators of their level of consciousness. Now, on to my (admittedly biased and based on speculation) answer.
I find the scenario of an actual "hot WW3" quite unlikely. We have reached a point where our weapons are simply so destructive that using them without restraint they would destroy all of humanity. This became clear from the day the first nuclear bomb was dropped, and since then technology has only accelerated. Most of what is practiced as "hot" war today is not all-out-carnage with supertechnological arms but either 1). Strategic, guerilla warfare like drone strikes, stealth bombing, etc. or 2. tribal warfare like genocides in Africa and other places.
Now, war in its more general sense of conflict will exist forever, but it becomes more "civil/subtle" over centuries of the evolution of consciousness. At least, as an average. There will always be anomalies like serial killers that are caused by energetic aberrations. In general, warfare becomes more mental, psychological, and covert rather than physical, emotional, and overt. We see this occurring with the trend of people inventing terms like "microaggressions" which would have been completely laughable in past decades because it is an idea of harm on a subtle level. (Of course, it can also be the expression of false and toxic victimhood, but I am just using it as an example to show where we are at.) In the medieval ages we were literally stretching people's limbs until they snapped on horrendous torture machines to punish them for crimes.
This is an indicator that humanity as a whole is on the incline when it comes to becoming more sensitive and compassionate, though we have a very long way to go before you can say we're a "peaceful species." Much of the war occurring in the world today is growing pains of this hyperevolutionary process in which our collective intelligence continues to increase while our physical bodies do not change nearly as much. It also gets into speculation about DNA activation, where areas of our genetic code seem to be "coming online" gradually.
TL;DR In my view: huge, physical, global catastrophic war is becoming obsolete as humans accumulate more understanding of reality, even if it doesn't seem that way. The process is gradual and there are many obstacles along the way.
I can agree with you on the fact that we are less barbaric in the ways we conduct war nowadays but, not with how you said that we are getting more compassionate. I mean we, "the general population" are but, those in power, the ones orchestrating the wars aren't. Not even a tiny bit. They have been and will always try to push wars onto us as they bring insane profits for them.