First things first: this is not a typical comparison with censorhip as background. Instead, it is a comparison of the original and the extended version.
In the year 2000, the game was released as "Code Veronica" for Sega Dreamcast. One year later, it was released for PlayStation 2 as "Code Veronica X". "Code Veronica X" is the extended version. The following comparison focuses on the differences of the original and the extended version.

I. OPENING AND MAIN MENU
The opening before the main menu screen is different.

Code Veronica	Code Veronica X

In the PS2 Version, the Battle Mode is available from the beginning On Dreamcast, it is not until the game has been completed.

Code Veronica	Code Veronica X

II. WESKER VS. CLAIRE
Claire encounters Wesker in front of the mansion for the first time.
Wesker: Greetings, you must be the lovely Claire Redfield.
Claire: Who are you?
Wesker: Let's to say that I'am a ghost. Coming back to haunt your dear brother.
Claire: Wesker!

Wesker: It seems that not much explaining to do is there. I was the one who attack this Island, who the fault you be hanging about. All too better for me, now that the cat dragged in this nice surprise, your ever so caring brother definitely show up. I must thank you for being such good bait.
Claire: I don't know what went on between you two but you had him all wrong. My brother is not the kind of person you think he is.

Wesker is choking Claire.
Wesker: I despise Chris!
Claire: What are you gonna do to him?

A further punch slings Claire away. Wesker approaches her and gets on her shoulder.
Wesker: Oh, how your brother will weep to see you die.

Wesker is getting a message.
Wesker: What? What is it? Stay there, I'm coming.

Another kick in the face and a few friendly words. Then he turns around so his glowing eyes can be noticed. Last but not least, he superhumanly leaps over the wall and vanishes.
Wesker: It appears you may be at some further use to me. I'm going to let you live a little longer.

III. WESKER SEES CHRIS
Since Wesker doesn't talk to Claire in the Dreamcast Version, he is surprised to see Chris. As a result, his comment when he is standing next to the monitor is different.
PS 2: Chris, oh little fishy. Come see my hook.
Dreamcast: Chris! You are here?!?

IV. WESKER VS. ALEXIA
At the mansion, Wesker encounters Alexia. For the first punch at Wesker, a different angle is used. While Wesker hits the ground in the Dreamcast Version, he winds up on his feet in the extended PS2 Version.
Dreamcast and PS 2:

Code Veronica	Code Veronica X

Now, the versions continue differently:
Dreamcast:
Chris for a second, then Alexia. Meanwhile, Wesker pull himself together and says to Alexia "Wow, what Power.".

Code Veronica

Alexia jumps at Wesker and slaps him again.

Code Veronica

Subsequently, Alexia turns to Chris and Wesker takes the chance to escape.

Code Veronica

PS 2:
Wesker looks at Alexia, she jumps at him and he ducks.

Chris keeps watching.
Wesker to Alexia: "You are coming with me!"

Alexia fires off a ray, Wesker dodges and starts a counter attack: he punches her.

It is Alexias' turn again but Wesker jumps aside and Chris is forced to get out of his hideout spot.

Wesker discovers Chris.
Wesker: Chris!
Chris: Wesker!

Alexia throws a punch in Wesker's direction, then she slowly approaches.

Wesker to Chris:"Chris, since you are one of my best man. I let you handle this!" Then he leaves.
From now on, the versions are back in sync plotwise, the shots remain different though.
Dreamcast and PS 2:
Chris is running to the stairs and Alexia fires off another ray at him. The the fight wit Alexia starts.

Code Veronica	Code Veronica X

V. WESKER VS CHRIS
After Alexia has been defeated, Chris escapes and encounters Weskers during. Wesker has put a stranglehold on Claire.
Claire: Chris!
Wesker: Move!
He pushes Claire away in the process.
Chris: Claire, no!
Chris goes after them.

During the chase, Chris comes up against a few zombies. He either runs past them or pushes them to the ground.

When Chris has caught up with them, a longer dialog follows.
Claire: Chris!
Wesker: Well done Chris. It turns out that Alexia's work wasn't much of anything. So now, the only thing left is revenge.
Chris: Let her go, Wesker! You don't want her.
Wesker: Fine!
He pushes Claire in Chris' direction.
Chris: Claire!
Chris helps her up.

Wesker: Today is a good day. I came for Alexia but killing you is even better!
Chris: Sorry to dissapoint you but Alexia is gone.
Wesker: That's no longer a concern to me, I have Steve to work with!
Claire: What?
Wesker: Steve, in his body there still ia a living T-Alexia-Virus. Steve should be a good specimen. Maybe he'll come back alive, just decided and be able to see your sister again.
Chris: You freak!
Claire: Don't you touch him!

Wesker: I'm sorry sweetheart but my men already took him.
Chris: You get out of here, Claire.
Claire: But what about...
Chris: As a surviving member of S.T.A.R.S., I have to finish it.
Claire: OK, remember your promise.
Claire vanishes.
Chris: I'll end it once and for all. Say hello to my comrads you've killed.
Wesker: I don't know where you get your confidence, Chris.

Now, Wesker approaches Chris. Then they fight.

Cut to Claire on her way to the jet while Chris is lying on the ground.

Back to Chris and Wesker. Chris is on the ground and has to take some punches by Wesker.

Wesker: Sure, I'm not human anymore, but just look at the power I've gained.
Then a power punch.

Chris notices the steal bars above while lying on the ground.
Wesker: Magnificent, don't you think?
Wesker jumps at Chris who manages to dodge it. Then he burries Wesker by flipping the switch underneath the steal bars.

Wesker can easily free himself from the bars. Then they are facing each other again.
Wesker: Nice try!
Chris: Wesker.
Then an explosion.

Wesker gets a face injury from the explosion and the two of them are being seperated by fire.
Wesker: Today is your lucky day. Next time we meet, don't count on another.
Chris: Next time...
Wesker: Until we meet again... hahaha.
Subsequently, Chris escapes and the self-destruction mechanism of the facility automatically activates.

After confronting Wesker, Chris runs to the elevator. In the Dreamcast Version, he runs over there after defeating Alexia. He runs a bit, then he punches the switch in order to flip it (his hand is shown sideways, the 2nd screenshort is very dark and out of focus I'm afraid). Then the flip.
Dreamcast and PS 2:

Code Veronica	Code Veronica X

VI. STEVE'S HAIRCUT
Steve's hair is different. This has even been considered for "Monster Steve".

Code Veronica	Code Veronica X

VII. ENDING
In the PS2 Version, the ending is accompanied by new music. Furthermore, the Dreamcast Version only contains little pictures while there are small videos in the PS2 Version.