Olympus Has Fallen:
The White House is taken down by North Korean terrorists, whose goal is to remove the US troops from the Korean Penisula to allow the civil war to end between North and South. Kang Yeonsak (played by Rick Yune) believes without the interference from America, Korea will be motivated through his own hope for a reunification of Korea as a whole.
He's also motivated by the vengeance for the death of his parents (mother is killed by an American landmine and father is execusted for crimes against North Korea) and seeks the access codes to the system called Cerberus, which allows remote access to all the nuclear warheads across the United States. His added incentive is to self-detonate the nuclear warheads in their silos leaving America an irradiated wasteland.
White House Down:
The White House is taken down by domestic terrorists, lead by Martin Walker, Head of the Presidential Detail and Secret Service Agent (played by James Woods). He's motivated by the death of his son due to a botched black ops mission and views this as a suicide mission due to him being diagnosed with an inoperable tumor as well (if you have to die, why not be for revenge, right? I guess?).
At the beginning of the film, President James Sawyer (Jamie Foxx) has announced a proposed peace treaty between all allied countries in the removal of military forces from the Middle East. Walker's goal is that of a $400 million dollar ransom with the hostages taken by the hired mercenaries as well as using the President's biometrics to activate the nuclear football from which he plans to use all of America's nuclear warheads to completely nuke all of Iran.
The added twist is that the real mastermind of the film is Speaker of the House, Eli Raphelson (played by Richard Jenkins) as through a series of events he's sworn in as the President of the United States. Once sworn in he pages Walker the nuclear launch codes to fulfill their plan, put the troops back in Iran, and remain President forever-ever (because sometimes one "ever" isn't enough). (Just in case you missed it, yes both James Woods' and Richard Jenkins' characters both still use pagers in the film.) Raphelson's motivations are based on the military contract companies he's (secretly/not secretly) associated with who supply both sides with weapons and President Sawyer's proposed peace plan would hurt the obvious monetary gain through war.