Snow and Rain

George W. Bush and Barack Obama
First, both Bush and Obama used expansionary fiscal policy to combat recessions by stimulating economic growth. As a result, they were the biggest contributors to the Federal debt. Bush added $5.8 trillion, while Obama added $5 trillion by the end of FY 2013. For more, see Debt by President.
Second, both Presidents spent more on defense than any prior Administration since WWII. For more, see Military Budget.
First, Bush created the two unsuccessful wars in Iraq and Afghanistan. Obama successfully found Osama bin Laden, allowing him to end the war in Afghanistan. He also ended the Iraq War.
The second biggest difference is that Bush did not regulate banks' use of derivatives, thus creating the 2008 financial crisis. Obama pushed through theDodd-Frank Wall Street Reform Act, which does regulate banks. In addition, it regulates credit, debit and prepaid cards and ended payday loans with theConsumer Financial Protection Agency.
Although both President's used expansionary fiscal policy, Obama passed theEconomic Stimulus Act. This powerfully created jobs through education and infrastructure, ending the recession in 2009. Bush used tax cuts, which aren't as effective in creating jobs. For more, see Unemployment Solutions.
Bush also spent $350 billion to save the banks with TARP, but did nothing for homeowners. Obama used TARP funds to subsidize homeowners stuck with upside-down mortgages.
As for health care, Bush passed the 2005 Bankruptcy Prevention Act. This made it difficult for people to declare bankruptcy, so they took money out of their home equity instead. After the Act was passed, mortgage defaults rose 14% per year. The number #1 cause of bankruptcy is medical costs(Source, NBER, Did Bankruptcy Reform Act Cause Mortgage Delinquency to Rise?, March 2010)
In addition, he created the Medicare Part D prescription drug program, which left a "donut hole" in costs to seniors.   It also added $550 billion...