Are there still wars, poverty, etc. Of course. However, how many wars have we had in the last 100 years compared to the wars of 1000 years ago. The difference is that we have had less wars but have caused more destruction due to the increase in technology
As a slight aside, this is wrong. The number of conflicts with 1,000 battle deaths in the 20th century is more than in the 19th century. Of course, there weren't very many wars with over 1,000 battle deaths 1000 years ago possibly due to a much smaller population (the EU today has 500 million citizens, the world 6.6 billion; 1000 years ago the pop of europe was something like 30 million iirc).
That said, there have been ~230 conflicts in the 20th century (a quick count from wiki's list; my source, "Capital, Coercion, and European States" has a higher number, but I can't check it right now). Wiki has 17 wars from 1000-1099. There has not been a single year in the 20th century without some conflict somewhere.
What has changed is duration. Civil and guerilla wars are increasingly longer than they were, while other conflicts have become shorter.
Destructive power, as you note correctly, has indeed mushroomed. That book I can't check (had to return it...urgh) mentions something like 46 deaths per 10,000 people in the 20th century. The 19th? 9 deaths per 10,000. I can't remember if that was just counting males or if it was 10,000 or some other number, nor can I remember what specifically he was doing with the numbers. When I get another copy of the book from the library, I'll update those numbers.
Point is, the 20th century has been the most violent in human history, not merely in terms of number of wars, but also percentage of death