Two recent decisions by lower federal courts illustrate a big difference between how the court systems in the U.S. and Germany operate, at least the constitutional courts.
In Germany, the Basic Law allows for individuals to apply directly to the Constitutional Court if they believe state actors have violated one of their constitutional rights. This centralized form of judicial review has the advantage of avoiding the problem raised by the title of this post: namely two lower courts applying the constitution to similar facts in a different manner.
In the United States, on the other, where the constitution does not explicitly call for the creation of a constitutional court, questions concerning whether one's constitutional rights have been violated by state actors are answered by lower federal courts. The result, as is often the case, is a similar set facts can come before two different courts, and these courts can come to polar opposite conclusions.
Andrew Cohen's recent article in The Atlantic entitled "Is the NSA's Spying Constitutional? It Depends Which Judge You Ask" highlights how a decentralized system of judicial review can be messy at times. Of course, both the lower court decisions to which Cohen is alluding will be appealed, and eventually an important question of constitutional law like this one will be heard by the nation's highest court, the U.S. Supreme Court, so even in a decentralized system of judicial review, important questions of constitutional law are eventually settled.
For more on these NSA cases see Cohen's interview on PBS news and this article in the Süddeutsche Zeitung.