Now, to answer your question: you could connect both phones to your computer and copy the pictures from the Android phone to your PC. Next, sync them to your iPhone using iTunes.
The texts are another story though. If you are with the same carrier you could request them to resend them to you. They keep copies of every message sent and received for legal purposes.
Say the police think the phone has been being used to traffic drugs. They would then get a warrant and the phone company would issue them copies of all the messages so they could look them over for incriminating evidence.
It isn't like there's someone at a computer 24/7 reading all the texts. They're just automatically saved on their servers for a reason like the one above.
OR - if your old phone is still active, you could just send everything in messages to your new one.
To send your pictures, using bluetooth is also an option.