Eh, somewhere between the two.
I'm kinda leery of saying definitely and for sure that global level conflict is a thing of the past, because the last time someone said that, they turned out to be very fucking wrong
To be fair though, the argument made was somewhat different between the argument people later said was made. Norman Angell actually argued that territorial war was economically irrational
due to the greater bonds of commerce and trade, and so wars of conquest were irrational and so would, if not disappear entirely, become much more rare than they had been throughout history.
Lenin, around the same time, had rather a different view. He instead argued that WWI was the consequence of a capitalistic world system vying for control of colonial resources. Because this stage of capitalism required large, state-backed monopolies, these monopolies would exert control over their nations politics to subsume and drive out other state-backed monopolies. Against the socialist thinker Kautsky, who argued that nation-states would form a joint federation for the exploitation of said resources (EU, IMF, World Bank anyone?) he believed the balance of power between nation-states in the existing system, the sudden rise of Germany and Japan, meant the system was unstable and that would cause the Great Powers to act rashly.
Most importantly, and a factor both Lenin and Angell left out of their analysis, is that Empire led to prestige. The leading powers of the period, the United Kingdom and France, had massive colonial holdings. They were allied with Russia, who had built a vast subcontinental Empire reaching down into central Asia. Italy and Germany were upstart powers left scraps, as they saw things. This was especially humiliating to the Germans, who were still managing to economically compete with the United Kingdom. Also Japan, who despite striking a powerful blow against Russian interests in the Far East, would never be treated as equals by the European great powers. Austro-Hungary had an empire, of course, but it was dying, being pulled apart by nationalistic rivalries which its leaders hoped war could solve, forging a common imperial identity through shared experience of battle. The Ottoman Empire was in a similar position.
It's fair to say that the world system today is different, at very least in the territorial sense. Since WWII, territorial borders have become pretty stable, by historical standards, helped by the occasional intervention against those who carried out such blatantly imperialistic policies (Desert Storm, for example).
There has been an argument made that global conflict has become "sub-rationally" unthinkable, which to a certain extent I agree with. It is very hard to imagine the UK going to war with France without a whole lot of other unforseeable and unlikely events beforehand. Nuclear war is the ultimate "unthinkable" conflict - lots of states have nukes, sure, but they plan to never have to use them, a practically unique development in the history of warfare. No state will even dare say for sure that it would use nuclear weapons first in a conflict, only going as far as saying they would "reserve the right" to.
But at the same time, there are still disturbing possibilities.
The big one is America-China, of course. China's growing economic power, growing much faster than the US, means there are worries that said economic advantage would be converted into a military one. China and America constantly develop weapons systems clearly aimed at each others' countries and state military doctrines and policies which suggest mutual mistrust.
At the same time, however, going to war would be an economic disaster, and there seems little in the way of an end-game plan for either state. Assuming nuclear weapons are not used, any such conflict would likely not resolve anything, because at the end of the conflict the US and China would still be there, most likely with the same ruling classes controlling the nation's politics. China is simply too big to just vanish, and so is the USA. At the most, one could hope for a powerful military strike that would cause one state to fracture and dissolve...but I just can't see that happening without nuclear weapons. And it could cause more problems that it would solve (Chinese warlordism, rogue nukes, American business partners in Korea, Japan, Thailand etc put under greater threat, loss of a unified China as a market etc).
America, as you may have noticed, tends to restrict its wars to places where they will cause minimum market disruption.
But, that said, both American and Chinese nationalism has a nasty anti-the other side component to it. Chinese nationalists see the Americans as being in collusion with the Communist Party, and frequently idolise groups known for their strong anti-Americanism, such as the Nazis and Russian Eurasianists. And I'm sure I don't need to into the whole Tea Party "China is to blame" fetish, enabled by foolish statements by standing government officials in both parties.
Japan and China is of course another one. Despite the supposed anti-militaristic constitution of Japan, since the 1990s it has been an explicit part of American pacific strategy to enable Japanese military growth to threaten China in the event of war. I don't think at the time Washington and Tokyo were wondering whether Japanese nationalists would make use of this, but they should have been. I've documented elsewhere how prevalent the Yakuza are in Japanese politics, and how the Yakuza are essentially an outgrowth of Japanese fascist secret societies which existed in the 1920s and 30s. The main party over there may call themselves the Liberal Democrats, and Japan may be on paper a democracy, but in reality it's a one party state, a good 96% of the time. That party is the LDP, and the LDP gets no small amount of its funds from Yakuza sources.
And of course, anyone paying attention to the news knows there are outstanding territorial issues between Japan and China, which feed into negative nationalistic impressions of the other side. Again though, I don't see it culminating in actual conflict, not unless something really drastic changes. China clamped down on its own nationalists, and despite increased military spending, Japan still doesn't have anything like the professionalism or discipline of the Chinese military forces (the JDF is still a civilian body, meaning it doesn't legally have any soldiers, meaning they can quit at any time). And trade between Japan and China is good, the occasional bout of poisoning aside.
Russia's another big one. Like all the aforementioned, it has crazy nationalists, a large enough population to possibly sustain total conflict, and a large economy. However, for the most part, Russia is concerned with asserting dominance over the Near Abroad and maintaining its place in global affairs. Some nationalists do call for reasserting the Russian Empire, on some terms or another, but by and large the Russian elite are prepared to play the game the way it is played in the 21st century - make lots of money, use the money to influence other states rather than directly control them, occasionally use military force against small, isolated states and talk a big game. In a Russian context, it seems content to carry out military operations only on small states that border it and that no-one will rush to the defence of - most notably Georgia.
This could, of course, backfire. It was a small, isolated state whose actions helped kick off WWI, after all. Georgia is being considered for NATO membership, and while I think the recent war means those plans have been shelved, for American nationalists, George is apparently a cause worth risking war with Russia over (see: McCain, practically everyone writing at National Review and Weekly Standard etc). But it seems most of the nations bordering Russia realise that getting too involved with NATO actually increases their chances of being the front line of any conflict with Russia, rather than enhancing their security, so they are not really all that committed to joining the organization.
And, of course, there are many other potential flashpoints. An India-Pakistani war turning into an Indian-Pakistani-China war, which then metasizes out of all control with a Japanese-American-Vietnamese intervention. In fact, that actually seems the most likely condition for another global war to take place under. But it does it seem very likely to you? It doesn't to me.
All these scenarios are possible, but if I had to give you the chances of them occuring tomorrow, I would put it near zero. If it was over the next 10 years, it would still be near zero. Over a hundred...well then, there are a lot more potential unknowns, and lower odds become less unlikely over large enough timespans.
Most people seem to have actually realised that gigantic, total war style conflicts are really really bad. Which is progress. Making money and occasionally whacking a small nation to sate the appetite for a bit of nationalistic destruction is a much safer and more sensible course of action.
But not everyone is sensible. They either miscalculate how far the other side can be pushed and the pressures it is operating under, or they think they are smart and powerful enough to mitigate the possible negative outcomes of their actions. It seems very rarely do we have both problems at the same time, but it is nevertheless possible. And if I had to name a prime contender for this state of affairs in the near future, it would be the USA, with a Tea Party influenced foreign policy out of the White House, taking a very negative tone with both Russia and China, combining unilateralism with reckless militarism. I don't think China or Russia would react, beyond possibly Putin engaging in some mockery, and that would constrain US options on its own, but if American nationalism were somehow able to interact directly with Chinese and Russian nationalism, it could set off nasty chain reactions which would in turn force their government's hands.
And that would be something we would possibly not all live long enough to regret.