I'd agree that W. Bush and other Republicans also downplayed the threat of Islamic terror. And they were equally criticized by Republican conservatives for their softpedal on terrorism.

The difference between Republicans and Democrats on terrorism is that while Bush also downplayed Islamic terror in his public comments, W. Bush still took a hard military stance against terror, hit back HARD immediately at Afghanistan, and also acted decisively against Iraq in March 2003 (with Democrat Senate approval 6 months in advance by the way), acted decisively in forming the Department of Homeland Security, acted decisively with the Patriot Act (the latter two I'm not fully on board with), approved enhanced interrogation, and locked up Al Qaida and Taliban prisoners in Guantanamo Bay.

Whereas Democrats tried to de-fund U.S. military forces on the battlefield, negotiate with Iran and other enemies, while alienating countries that are our allies, use drone strikes to kill, but take no Al Qaida prisoners that can give us information.
Democrats free the most dangerous prisoners from Guantanamo in lousy deals, that allows them to return to the battlefield and kill more U.S. soldiers and civilians. Republicans would keep them locked up until the war ends.
Democrats prematurely exited Iraq and lost all the hard-gained victories, enabling ISIS to take half of Iraq in just a matter of weeks. And 8 months later, has still done nothing about ISIS.
AND NOW OBAMA IS READY TO PREMATURELY PULL OUT OF AFGHANISTAN AND LET THE SAME THING HAPPEN THERE!

Democrats made public our prisoner interrogation playbook, so now Al Qaida prisoners laugh with defiance when they used to snap and provide information, with no torture given or required.
And actually try to prosecute CIA agents for simply doing their jobs!

On every conceivable level, Democrats have proven themselves weaker on Islamic terrorism, and on national defense as a whole.