There is, in my mind, a key difference between the two theories in that the "European Civil War" is an attempt to explain reality in light of our present perspective rather than the perspective relevant at the time. I consider this a form of presentism.

The Second Thirty Years War Theory
The "second thirty years war" theory does not in the same sense reinterpret events in a modern perspective. This causes a lot of problems in explaining how we accout for an effective "22-year cease fire" in the middle of the conflict and as such serves to highlight how the European Civil War theory really only works if we accept the reinterpretation of events in a modern light.

Both theories seek to expand upon the fact that all conflicts are in some sense related to one another but in my opinion overstate the importance of these connections in an attempt to strengthen the theories. For example, a key argument in Churchill's definition of the term is that Hitler's foreign policy was merely a continuation of the previous foreign policies of Wilhelm II and Bismarck, an argument that in my opinion doesn't survive close scrutiny. Henig argues against this perspective in "The Origins of the Second World War" and does so quite well in my opinion.

A second key pillar of the argument for a Second Thirty Years War is the view that the treaty of Versailles was a principal cause of World War II. I personally think that this argument is effectively refuted by Bell in The Origins of the Second World War in Europe where he effectively shows that a peaceful renegotiation of the harsh conditions of the Treaty of Versailles were already well underway by the mid 1930's. He also demonstrates quite clearly that it was Hitler's ambitions and long term plans that made such a renegotiation impossible, not the Treaty itself.

The European Civil War Theory
Reinterpreting past events in a modern light allows the use of some modern terms and models that allow us to account for certain problematic aspects of the Second Thirty Years War theory like a 22-year cease fire and why we link the first and second World War but not the Franco-Prussian War. It does so by utilizing a wider perspective than was common at the time and is as such similar to the Long War theory.

Like the "Second Thirty Years War" theory there are many problems with the European Civil War theory. For example, the role of the United States in both world wars is highly problematic and there is little or no consensus on how the theory can or should be used to explain other related conflicts such as the Sino-Japanese Wars and European colonial proxy-wars.

Another problem is that the European Civil War theory causes a need to redefine some of the included conflicts (the Spanish and Russian Civil Wars for example) as "National Civil Wars" in contrast to the "International Civil War" that is the European Civil War. It is also difficult to explain the global nature of parts of the conflict within this model.

The theory really only makes sense if we view the conflicts in light of todays relatively culturally, economically and legally uniform Western Europe. Even then, it is a model of limited utility as it creates more problems than it solves, for example, one would have to demonstrate that such uniformity existed prior to the "European Civil War" for the theory to make sense, something I have yet to see done. It is entirely possible to explain the emergence of that uniformity within the framework of traditional historical models.