I traded in my my first iPhone (a 3GS) for the 4S last fall after two years. I just went over the 2GB data limit included in my plan for the first time last month, so there's no question in my mind that the 4S uses more data.
To be clear, I wasn't using tethering or anything that I would think would use a lot of data either.
Why do I think my data usage has risen roughly 5x?
1) Apple has raised the data caps for 'over the air' downloads to 50MB: For the first time, I can download most, if not all, of the podcasts I listen to over the 3G network, instead of using Wifi or plugging into iTunes. I used this functionality at least two or three times last month, so it is likely that added 100-150MB to my data total. So whether you are updating apps or downloading media from iTunes, this can add up quickly.
2) iMessage: Since most of my friends are on iPhones, I am sending a lot more iMessages than normal SMS messages now. I sent almost 750 'texts' in December, and that number dropped to 128 in January. I have been averaging about 50 per month since then. Particularly because you can send photos through iMessage, this is something I need to be careful of. See reason #3.
3) The camera: The pictures I took with my old iPhone were usually pretty bad. Having a flash and better focus makes it a lot more likely that I will share photos on Instagram etc. For example, I went to an Orioles game on opening weekend, and uploaded a few images to Facebook. Plus, sharing a photo with some one who has a similar phone tends to make the viewing experience better.
4) Streaming: I'm fairly sure that my YouTube and Facebook streaming to my phone are up, although this is hard to quantify.
5) Siri: This is a fairly small part of the equation for me, but if you use it a lot, it will add up.
I can think of a few other reasons that my usage may have been slightly higher in this month (March Madness?) but I think these three are the main ones for me.
Have you seen your data usage rise with a new phone? If so, have you taken any steps to avoid going over your plans limit?
Update: Was interested to see that AT&T's average bill has gone down from $88 per month to around $80. I assume this is because people are using less minutes and more data.