Just upgraded from my 4S to 5, 2 days ago. Noticed this same symptom right off the bat.
Here's some background... I restored via iTunes from my 4S. I have message notifications turn off on the lock screen so I don't see what is being texted.
I've done the following:
If i'm in a message with person A, and just hit the top button to black out the screen, and person A texts me back I will receive no audible notification however the text arrives.
In the same scenario if message with person A is up, hit the top button and screen goes black but person B texts me, I will receive an audible notification.
If I'm texting person A, then after I sent my text and I hit the home button so that person A text history is not actively on the screen and then I receive a text, I will get audible notification.
I've also tested putting the baner notification back on. Guess what? I get audible notification. I turn it back off, nothing.
I'm going to reset my phone back to stock, and manually configure the phone with no restore. I want my phone to not display incoming texts but still provide audible alert on every single one.
I started on iOS 6.0.1 and saw there was an update to 6.0.2 so I updated hopting it would resolve the issue, it did not.
YMMV and HTH