Well, speaking to dis/advantages to unification, it somewhat depends on the size of your projected opponents and their likely methods of attack. Small countries with potential enemies on the borders, like Israel have very different needs from large, isolated countries, like the United States.
A perfect example of the mobilize-quick-and-fight-like-hell force is the Israeli Defense Force, pound for pound the best “small” armed force in the world, in my humble opinion. The IDF is unified and specifically designed for defense, and offense, at all points of their borders. They can mobilize fast, coordinate air and ground units quite well, and deliver considerable firepower to specific areas in need of holding, all under a tight, unified command structure. Thus, Moshe Dayan was able to commit all available forces to blunting the suprise attacks of the 1973 Yom Kippur War without having to worry about interdepartmental squabbling and resource allocation. Within a week or two, the IDF had reversed the attacks of Egypt and Syria, was across the Suez Canal, and blasting its way down the road to Damascus before the Russians started rumbling about nuclear defense.
But, like many nations out there today, the IDF is a UN-dependent force: their intention is to be able to defend themselves for a relatively short length of time, and blitzkrieg areas of enemy territory for the purposes of post-battle negotiation. They depend heavily on outside intervention by either the UN or other interested parties, as happened in 1973. A large protracted war could be fatal, as it is unlikely that Israel can replace their material needs themselves.
Disturbingly, both India and Pakistan have built their armed forces on a similar principle. Both nations have opted for fast-mobilizing forces with large offensive potential, with streamlined command structures and fast-moving forces that rely heavily on armaments procured elsewhere. Both nations appear to have offensive strategies designed to snap up as much enemy territory as possible within a few weeks on the assumption that foreign nations will step in to moderate the conflict. Unfortunately, both also have The Bomb, and it is now unlikely that foreign nations will be able to threaten the combatants into an armistice. That’s a recipe for the worst kind of disaster the human world has seen.
America, Russia, and to some extent England, on the other hand, are very different. All enjoy a certain amount of isolation (Russia through vast distances of frontier country, the others courtesy of the oceans). All produce a majority of their own weaponry. Therefore, the largest immediate threat these countries face, arguably, is from within: all three nations have experienced civil war, two of them comparatively recently. The primary objective is therefore to prevent the military from being able to threaten the government, or at least reduce that threat. Keeping large divisions between branches is one way of doing that.
In the event of war, these countries have the luxury of carefully assembling overwhelming force which, while appearing on the field much later, can shift the balance of any coalition war. But they are often delayed by requirements of production, training, and transit. In World War I, the United States declared war two and a half years into the conflict and didn’t arrive on the field in force until almost a year later. When they did, the war was over in six months. The US was a declared combatant for only three years eight months of the six years of WWII, and didn’t begin exerting any appreciable pressure against their enemies for some nine months after Pearl Harbor, but they played a major role. Similarly, the Soviet Union could do little but defend itself for a year after Germany’s invasion during WWII, but war production stepped up enough to counter Germany’s forces and eventually totally destroy them.
Desert Storm, which might be characterized as a “big guy” style war in character, required months of Desert Shield to make overwhelming victory possible. In that war each branch of the DOD made its own arrangements for transit to Saudi Arabia, although unprecedented cooperation was implemented.
So, to sum it up, if you are a small country facing immediate threat, follow the model of the IDF and back it up with a crack diplomatic staff and some big, mean friends. If you are a large isolated country, follow the example of the Brits and protect yourself from threat within by subdividing your military. I wouldn’t dare claim that I’ve touched on all of the reasons for subdivision, but the above is a prominent facet.