Instead of saying anything negative(because there are a lot), I will just mention the good points.
OLYMPUS HAS FALLEN:
1. It has Gerard Butler as Mike Banning, the HERO. Gerard is one of my Hollywood crushes...sigh
2. Morgan Freeman, Aaron Eckhart, Dylan Mc Dermott, Angela Bassett and Finley Jacobsen were superb!
3. Nothing beats the "original"
WHITE HOUSE DOWN:
1. The story is very believable and has integration. The actors were ALL great.
2. I didn't "see that coming"
3. Channing Tatum is hot!
4. Joey King is a darling
5. James Woods, Maggie Gyllenhaal and Richard Jenkins are so convincing.
6. Jamie Foxx is very charming.
7. I like the fact that the President has more action scenes here
Lesson: Never look down on flag twirlers ;-)
1. Target: White House/President of the United States of America
2. Inside Job
3. Hierarchy :p
1. Perpetrators and purpose/mission
2. Though both have cute "children" in the story, Emily Cale in White House Down(Joey King's almost 14 in real life, but she's playing the role of an eleven year old girl) is the daughter of the hero, John Cale. Connor in Olympus has Fallen is the son of the President of the United States, Benjamin Asher.
3. The race of origin of the President, but that's immaterial
4. Mike Banning was a disgraced Presidential Guard while John Cale was a rejected applicant who became a White House tourist along with his daughter from his estranged wife.
5. There was a lighter feeling when the movie was over with White House Down(PG 13) and a heavy feeling after watching Olympus Has Fallen (R18) even if it was victorious.
For other differences and similarities, just search the net. I'm sure others did extensive comparisons. I just simplified it. ;-)
Here are some links to "help" you: