It's not just a matter of which quotations one uses. The principal difference is that there's a standard way of analyzing the Quran and hadith for nearly 1400 years (to be exact, there are a few different ways in which to do it, but the ways and the results don't vary greatly when it comes to issues of war). You use this verse or hadith in this circumstance while neglecting others, etc. The first link is based upon the standard method of analyzing. The second uses current events and tries to justify them using quotations as they see fit. It's easily documented the atrocities committed by Muslims. They try to show that it's inherent to Islam and Islamic law. The only way to truly analyze the Quran as a Muslim should is from a classical perspective. That's why those who commit terrorism are doing it outside of Islamic guidelines, they take the verses and traditions that they want to use and ignore what they don't. It's been happening for a while, first with the Kharijites and now with modern day terrorists.