I will begin with the assumption that you are asking about these time periods from the point of view of the United States.
The position of the United States in the world was very different in the early 1900s. At that time, the US was a relatively minor power that was just coming into prominence on the world stage. Today, the US is the strongest country in the world, though it is coming under some challenges from abroad.
Domestically, the US is also quite different. The early 1900s were the start of the Progressive Era. This was a time when there were strong calls for more government intervention in the economy and society. Today, there is much less confidence in the idea that government can fix these things.
There are similarities between the two eras. In both, immigration was a major concern for many people who thought it would dilute traditional American society. In both, major economic changes were occurring and inequality was widespread. Even so, the differences are rather more significant than the similarities.
In both Europe & Asia, conflicts were all around with little resolution. The 20th century saw a lot of ends to countries and empires, such as the Qing dynasty in China, the British Colonial Empire, the Ottoman Empire, the Russian Empire (even the Soviet Union which was right after the Russian Empire) and many more. Compare it to today, We still see a lot of the nations that remain from the ones that have fallen.
Which then brings me to the "From the old to new" that the 20th century had rather then today. From the ruble of the fallen come the new strong countries that would follow. For example, After the Qing dynasty came a lot, and I mean ALOT, of political struggle and revolutionary uprisings. It wasn't until 1949 that China finally became unified under the People's Republic of China by Mao Zedong, however, it wasn't the best thing for China, but at least they became unified! And as we see today, China has become an Economic Power House on the world stage, though it came from years of blood shed and suffering.
With the rising of World Powers of today (which I consider to be most of the G.8, "Pfft! Canada?! LOL" XP) compared to how they were back then, you see that there was a rise. As pohnpei357 described how America wasn't even a world power back then as it is now goes to show what time will do to to nations and empires who are willing to stay and become stronger. Such as how Russia (at the time they were the Union of Soviet Socialist Republics or the U.S.S.R) became so predominately strong because of a need to industrialize.