Does it matter whether Catwoman chooses to save Batman or not?

I'm at what I assume is the end of the 3rd Catwoman mission. I've beaten down the guards, I have two suitcases full of loot, and I'm apparently having a moral dilemma regarding whether I should leave Batman buried under a pile of rubble or flee Arkham City with my ill-gotten gains.

Though she apparently doesn't have any affect on the main story, I'm not sure which I should choose in order to get the most out of the DLC.

Are the two options merely an illusion of choice and end up with you taking the same path, regardless of which you choose? More importantly, are there any achievements associated with either choice?

Solution 1:

Actually, since we are talking spoiler, check this video to see what happens:

Basically everything is ruined, Joker becomes an immortal and takes the city. The game ends, with Barbara Gordon crying out loud over a radio line.

But, if you watch it to the end, the game will rewind to the point of the decision, and let you choose again. :)

Solution 2:

Well, when I had to choose, I chose to leave Arkham City, but it re-winded back to when I had to chose. So, I had to chose to save Batman. Then, from there, you're Batman again and you have to stop Protocol 10