This is not intended as a "President Bush did everything right and President Obama is doing everything wrong" diatribe because this is simply not the case. The Bush administration, the DOD and all levels of the national security establishment such as the CIA made more than their share of errors prosecuting the GWOT.
The single biggest achievement of the Bush era was convincing Americans in the wake of 9/11 that we were indeed at war with global jihadists (I use the term militant Islamists) and their terror sponsors. The Bush administration unleashed the military and intelligence agencies to go on the offensive to "root out" the terrorists and "bring them to justice." Sophisticates complained about President Bush's simplistic approach and denounced it as "war mongering."
War is war, mongering aside - what was or is the alternative? The Taliban and al-Qaeda was shattered and driven from Afghanistan, and the Iraq regime was toppled and Saddam captured, tried and executed. Al-Qaeda has been decimated in Iraq and both countries are fledgling democracies in a region of the world where Muslim democracies are almost unknown.
By any standard these are the most significant foreign policy accomplishments since the end of World War Two. The leftist view is that it was all a dark and disastrous imperial adventure and marked the end of Americans' civil liberties. Although the absence of anti-war activists protesting the ongoing troop presence and deaths in Iraq and Afghanistan (with a few exceptions) since President Obama took office tells you all you need to know about the motivations and convictions of the left.
The Bush policies or "doctrine" if there was one was that the U.S. was at war and would not only fight terrorist organizations, but would attack rogue regimes who supported them. This was why the Taliban government and the Iraqi government were targeted and not just al-Qaeda. This was not "taking the eye off the ball" but an attempt to carry out a strategic response instead of a purely tactical tit for tat response that had failed during the Clinton Administration. During his eight years in office there were at least half a dozen attacks, including the first WTC attack, but cruise missiles were the only response.
President Obama is more a caretaker President than a war time President who feels obligated to continue the Bush policies in Iraq and afghanistan in the near term, but with an eye on the exits instead of a commitment to victory. He is essentially presiding over a holding action as he waits to be able to report to his base before the 2012 elections that he has pulled most of the troops out of Afghanistan and Iraq.
Predator drone strikes will not destroy al-Qaeda and the Taliban and will not convince them their cause is hopeless. President Obama does not believe the GWOT/overseas contingency operations are really worth fighting. He is more comfortable arguing about where and how captured enemy combatants will be tried and how Gitmo can be shut down or how sanctions will eventually make Iran's mullahs give up their nukes, but what about their ongoing meddling and killing of U.S. troops in Afghanistan and Iraq? This is not way to fight or to win a war.