The 3rd Birthday was originally announced as a cell phone game. To the great relief of pretty much everyone in the world, the platform was changed a couple of years back to PSP.
Some other changes accompanied the platform switch. Just check out the vastly different main visuals for the two versions.
To the left, the main visual for the cell phone version. At the top, the main visual for the PSP version.
As detailed by the development staff in an interview posted in Famitsu earlier in the week and today at Famitsu.com, the mobile version of the game was originally meant to be episodic. The main visual you see above was the visual for episode 0, and was thus meant to represent the start of the Twisted creatures' descent upon Manhattan.
The PSP version is a full, self-contained game. The main visual for the PSP version depicts a later point in the storyline, apparently when the Twisted have pretty much destroyed Manhattan.
Look closely, and you can see some similarities between the two images. Both show the Statue of Liberty destroyed (in the PSP version, you can see the statue head to the right of Aya).
See the thing that's surrounded the building behind Aya in the PSP version's main visual? That's a nest for the Twisted. It's named Babel.
Source: Andriasang