The emergence of modern weaponry--particularly military aircraft--is probably the greatest military comparison. Repeating rifles and machine guns were used extensively in WWI and their modern versions created a deadlier outcome in WWII. Tank warfare first began in WWI before becoming an extensive form of destruction (and transportation) in WWII. But the use of airplanes, which played a small part in WWI, became the dominant force in WWII. Aerial bombing not only played a major part of military tactics, but the decimation of strategic factories and the deadly force used on citizenry contributed to the end of the war.
I have to agree that the major similarity is that they both were about the balance of power. But, I want to also add that both relied heavily on the use of propaganda to create nationalism and support for the war effort, on both sides, in both wars. Regardless of our (America's) reluctance to get involved in WWI, eventually when we did get involved it was key that everyone do their part: every man sign up to fight and every woman and child keep the home fires burning. This same idea obviously applied during WWII. It is not just the importance of the whole nation pulling together (military and civilian home-front) in both wars, but the use of propaganda to get this done.
There are some great examples out there of posters and cartoons (some done by Disney) that show how US propaganda worked during both wars.
I was going to point out one of the big similarities was the way that the US got the chance to flex its muscle and find out that they could be a huge player, maybe the biggest player on the world stage and yet avoid any of the consequences that the countries in Europe had to face, particularly the Russians who suffered by far the most casualties and the most devestation outside the Germans.
It is a great source of pride and confidence for a people to be able to influence history in such a way and to have the populace generally unaffected (though of course I am not trying to belittle the losses and the sacrifice of those who lost loved ones in the fighting, etc.) But the cities and infrastructure of the US only grew and was improved while many other countries were being completely demolished.
You might want to think about the outcomes of both wars. Both wars led to a significant sense of disillusionment and apathy with the world as people had to cope with the fact that, in spite of all the scientific advances that had been achieved, humanity was still capable of killing its members in ever greater numbers. The sense of profound disillusionment after both wars is a notable phenomenon.
One similarity between the wars was that in both World War I and World War II almost every able-bodied man in the countries that were involved fought. This depleted the workforce greatly after the war, especially in Europe and especially after World War I. Almost an entire generation of young men was wiped out in countries like England and Germany, and the US fared only a little better.
The primary similarity between the two wars is that each was an attempt to first upset and then maintain the balance of power which existed in Europe at that time. The alliances which sparked the beginning of World War I did not exist until after hostilities began in World War II. Additionally, Italy and Japan swapped sides in the wars because their territorial demands had not been met. Territorial demands were an element in both wars; in fact in World War I, promises were made by belligerents to share the spoils of victory by awarding territory to their allies. In World War II, there was no such promise; rather it became something of a grab bag: Germany and Italy in Europe and Africa, and Japan in Asia.
The major similarity to me is that both were caused by countries trying to do away with the status quo in the international system. In both cases, the war came about because a country or countries wanted more power than it had in the international system at the time.
A major cause of WWI was the fact that Germany was trying to get more power than it had had. This scared many other countries (notably France, England and Russia) and made them want to go to war with Germany to preserve the balance of power.
A major cause of WWII was the fact that both Germany and Japan (and to some extent Italy) felt that they did not have the amount of power that they deserved. Germany wanted to regain the power it lost in WWI. Japan wanted to have a large empire and to be treated as a major power. The Allies resisted this because they were happy with the status quo.
So, I would argue that the major similarity is in the fact that the two wars were caused by very similar factors.