Just as secure as any other computer. Possibly moreso, but certainly not worse. If you use your laptop to go to Amazon you should feel fine to use your iPhone.
And even though it should be encrypted and safe, as an extra step I tend to limit shopping to times when I'm on my home Wifi or on 3G. I don't fully trust free public wifi because you don't really know who's running it. But I trust my ISP at home (Verizon) and my cellular provider (AT&T) enough to send sensitive data over their networks.