In the case of NATO, you start to become an expeditionary force and travel outside your theater to create some sense of purpose for the money it costs to keep you in existence. Of course that's not what NATO was envisioned to be so now the EU wants to form its own military.
An EU Army would have two potential advantages over NATO. One is it would be a way to formalize the participation of France (the only other European nuclear power besides the UK). Second is it would not be driven by the U.S. unlike the case with NATO. The down sides is without the U.S. all of the costs of the proposed EU Army would fall to the European countries, many of whom are balking at paying to participate in NATO.
The question for the EU is will the creation of an EU Army make the Kremlin even more concerned with Russia's border with Europe?
Similarly, the creation of an Arab Army is unlikely to call the already jittery nerves in Tel Aviv. Make no mistake, despite Mr. Obama's and Mr. Kerry's assurances to the contrary, the U.S. has much less to fear from Iran's nuclear program than does Israel. Israel is by most assessments considered to have nuclear although they officially remain undeclared. If the potential for Iran to become nuclear is enough for Israel to strike, what happens if at some future date the Arab Army decides to conduct exercises simulating a hostile Israel?