A1. They are basically the same. The game system is completely the same, both with battles and dating. The only thing that's different are the bonus scenarios and the bonus feature. The scanarios are:
PS2 = Geass, Order of the Black Knights, Britannia Military, Ashford, and Bonus: Blue Moon.
PSP = Geass, Order of the Black Knights, Britannia Military, Ashford, and Bonus: Japan Liberation Front.
PS2 version has another bonus: Theater Mode. It's for you to pick the lines you want to use and combine to create your own scenario. It's for fun and that's it.
The PSP Special Edition comes with an extra "Black Rebellion" UMD disc, which is a re-edit of the first season. C.C. is doing the narration. They did a good job in condensing 25 episodes into 2 hours. Some scenes have a different feeling because of the scene sequence and different background music. I enjoyed it very much. It's like a 2 hour movie. :)
Q2. I heard that the PS2 version is more girl-oriented aka "dating oriented", while PSP version is boy oriented aka "military oriented". Is that true?
A2. No. The only thing that's different is the bonus scenario. Blue Moon is dating and JLF is action-packed. For the main 4 scenarios, they all contain the same amount of talking and battles. Both versions are designed to be enjoyable to boys and girls.
Q3. What's the length of this game?
A3. For each scenario (or chapter) it's around 3~6 hours. There are more than 20 endings. So finishing them all would take about 60 hours.
Q4. Are the contents of the game canon?
A4. Here's Comments from Director Taniguchi before the game's release.
A. In one word it's "joyful". I've directed several shows, but Code Geass is the first that got made into a game of its own. It's something that brings joy to both the staff and the fans. Therefore in a good way it's trusted to Bandai Namco.
Q. There have been several meetings regarding the scenario. Did Taniguchi-san and Sunrise staff provide ideas?
A. Just like the mangas and novels, in order to make the best use of different media, we give them full freedom. However, to offer the fans the fun of imagination, we asked them to put some parts that can't be done in the anime into the game.
Q. Looking at the progress of the game, will we see connection to R2 or settings that will carried on into the anime?
A. Partly because it's released before R2 is on air, we came up with having R2 characters like Rollo and Knight of Rounds involved. As for how they are involved, please play the game to find out. Well, actually since it's not finished yet, I don't know for sure.
From the rumors I heard, there is/are character(s) who's really loved by the game development staff. I wonder how wild will their imagination run from the frame provided by the anime staff? This part will take some research.
It might look like I'm praising for my staff but... While the first episode of R2 is in progress, our anime staff Kimukata-san, Chiba-san, and Nakada-san also devoted a huge amount of effort into this game. Please enjoy it with R2 if possible.
This pretty much answers the canon/not-canon question.
Mangas, novels, and games are mixtures of background setting and stuff made up by the writers/game staff.
Q5. How to change the gender of main character?
A5. He's male and there's no way to change it. Actually this guy has a very good background story. So good that it's weird to view him as a nameless faceless character. ;_;
Q6. How do i save?
A6. You'll be able to save after finishing the prologue. Press □ at the map area. And there's auto save after each event.
Q7. The "title call (タイトルコール)", aka the voice that says "Code Geass Lost Colors" at the title screen, is different each time! How come?
A7. Yes. It changes with your progress. As you clear more chapters, more would appear. Voices known now are Lelouch, Suzaku, Kallen, Millay, Rivalz, Ougi, Diethard, Jeremiah, Lloyd, Mao, V.V., Euphemia, Dalton, and more.
Q8. I hear someone talking after the title call. What's that about?
A8. That's the mini drama between two characters. The content depends on who did the title call. for example, title call of Lelouch brings up the conversation between Lelouch and C.C.. Ougi brings up the chat between Ougi and Tamaki.
Q9. How to I choose different chapters to play?
A9. Here are the routes, with confirmed endings.
1. First time round:
Geass Chapter. No other choice. Possible endings: C.C., Lelouch, and Nunnally.
2. Finish the 1st round, save, and play again. When in Prologue:
Talk to C.C. → stay in Geass Chapter.
Keep talking to Kallen → she will introduce you to Zero → enters Black Knights Chapter. Possible endings: Kallen, Lelouch, and Diethard.
Keep talking to Suzaku → he will introduce you to the military → enters Britannia Military Chapter. Possible endings: Suzaku, Lloyd.
Keep talking to Millay and student council → Millay will invite you to be in charge of school festival → enters Ashford Academy Chapter. Possible endings: Lelouch, Nunnally, Milley, Shirley, and Suzaku.
3. New routes after clearing the Black Knights Chapter:
1) Hot spring vacation for Black Knights. Choose to "take some rest" (the option below) after the Narita battle. Possible endings: only one and that's a secret. ;) Remember, save before Narita and turn auto-save off during this route.
2) For PSP version, you can enter the Japan Liberation Front Chapter from here by ignoring Zero's orders in Narita and go help Toudou. Possible endings: Chiba, Kaguya, Toudou, China.
4. new routes after clearing the Ashford Academy Chapter:
1) Hot spring vacation for Ashford Academy. Possible endings: none.
2) For PS2 version, you can enter the Blue Moon Chapter from here by telling Millay you'd like to fall in love. Possible endings: C.C., Lelouch, Nunnally, Kallen, Millay, Shirley, Rivalz, Kaguya, and Euphie.
5. New routes after clearing Britannia Military Chapter:
1) Join Cornelia's guards. Possible endings: Cornelia & Nonnette, and Euphie.
2) After finishing Cornelia route, you can choose to join the Purists when playing this chapter again. Possible endings: Villetta, Jeremiah.
Most of the chapters have a bad ending. To avoid it, don't use Geass more than you really have to. But there are animations or CGs for some bad endings. So just try them once if you're aiming for 100% collection.