You know what's really weird? These two animes are almost identical! Thay are both really really good, but I still prefer Code Geass for some reson...
Anyways, here's some similarities I noticed:

~Main character is a guy in high school/college that is an absolute strategic genius with a little sister.
~This guy is fed up with how the world works and wants to change it.
~They acquire some otherworldly power that allows them to fulfill their wish of changing the world.
~They have some sort of being (who supposedly gave them their power) that stays with them and/or helps them.
~They lead two lives--a normal one, and a secret one (in which they carry out their plan to take over the world).
~Their best friend is actually their worst enemy who is trying to unmask and defeat them.
~They end up kiling their loved ones (by accident or on purpose) and become utterly alone in their quest for world domination (other than the supernatural being that stays by them).
~They die after completing their quest.

Here's some differences (sorry, this might be a little bit biased because I like Code Geass better than Death Note):

~In Code Geass, the plot includes more characters and actions that take place at school, while in Death Note school is the setting less than five times.
~In Code Geass, there is more physical fighting and mech fighting, while in Death Note the fighting is almost always phsycological.
~In Code Geass, the main character's best friend/enemy joins their side at the end and ultimetely completes the goal of the main character for them. In Death Note, the best friend/enemy's death is a key component in the success of the main character.
~In Code Geass, the main character's death is intelligently coordinated and is the last step in carrying out their plan. In Death Note, the main character's death is merely a sad way to exaggerate the theme and end the story.
~In Code Geass, there is a sort of follow-up at the end to show how the main character's diligence, bravery, and wits were used the the world's advantage. In Death Note, they don't explain if the world ever changed back to it's original state or if it was permanently improved.
~In Code Geass, there was a mid-point of the story where many thing drastically change and both the enemy and main character are sort of remade and far stronger than before (this is the part where it goes from 'Code Geass Lelouch of the Rebellion R1' to 'Code Geass Lelouch of the Rebellion R2'. This is probably because the Code Geass storyline is longer and more involved than Death Note. In Death Note, the storyline is continued in exactly the same manner the whole way through.

OK, so that's all I can think of right now...
If you think of something else, just leave a comment and I'll add it. Also, if I remember something else then I'll just add it in, too.
Hope you enjoyed! ^^