The dissolution of the United States into multiple entities in competition with each other would have brought British and French, and later German, intervention into the Americas, as the Monroe Doctrine would have become moot. Give me a break. The Confederate Army(P.A.C.S) of 1864 could have conquered all of Europe in 1864 if you gave them a sealift over there. THe Union could have done the same, only more quickly. The Europeans were in awe of Gen Lee and the ANV.
The
wartime Confederate and Union armies were the most powerful military force the world had seen since the fall of Napoleon. However, had the South won or the North acceded to secession, there would have been rapid demobilization, as America did after both world wars and the War for Independence and as the Union did post Appomattox. And who is to say that either the Confederacy or the Union would have remained intact? As Texas evolved from a cotton producing state to a cattle producing one, its interests would have diverged from the rest of the South. As I noted previously, the Union had several regions whose economic interests diverged sharply. Furthermore, its territory would have remained very large. Don't forget that the British and the French were on the Canadian and Mexican borders, respectively.
Only the preservation of the Union prevented the reassertion of European powers into the Western Hemisphere. The Germans, shut out of Africa and Asia by the British and French, would have found South America very tempting. Don't forget that hundreds of thousands of Germans emigrated to Argentina, Brazil, and Chile. The existence of two, and probably more, independent and rival nations on the current U.S. territory would have made the Americas a playground for the European powers. Perhaps they would not have re-colonized the former U.S., but they would have had wide latitude in Latin America.