A big difference is that now you learn (faster or at all) about issues that 30-50-100 years ago would have been completely obscure to most of the world, and you're getting the news hammered into your head on so many channels until you can only see them as important. So most issues today hit people far harder than they used to because the world used to be a bit more (unwittingly) ignorant and what you didn't know couldn't hurt you. Knowing about every bad thing everywhere, and knowing the impact of that can hit harder than the actual issue. It takes a huge emotional toll.
If issues command more attention time each day they feel more important. Generalplan Ost might have killed twice as many people at the same time as the Holocaust but most people never heard of it because it didn't get that much prime time. And the Bangladesh or Indonesian genocides flew under the radar for most people around the world.
Lots of things are possible but the likelihood, and the fact that this is hammered into your head via every channel make all the difference. Nuclear war is possible but if FB would throw this possibility at you every day I can guarantee you'd see it with very different eyes and feelings.
Just going back a few decades you had things like AIDS or the hole in the ozone layer. So each generation had their own burden to bear. And things like global warming aren't something that hit one particular generation (unless it triggers a catastrophic and quickly unfolding event), it just erodes away the niceties of life with each generation.