There's no reason we can't make these two get along.
If you're an iPhone user who wants to find out what that whole Android thing is about, there's really no better way to get your feet wet than to buy a Nexus phone. The hardware is never perfect, but Google and its partners will typically sell you a fair-to-good smartphone off-contract for about half the price you'd normally pay for one. It's a fine value proposition if you've already used your carrier subsidy to buy a shiny new iPhone 5S.
As someone who spent a lot of time jumping between an iPhone 4S and Nexus 4 (and now, an iPhone 5S and Nexus 5) as a daily driver, I've got a few tips to pass on to people who are interested in Android, but who aren't quite ready to make a permanent move, or for the people who want to stay familiar with both operating systems because their jobs demand it, or for the true tech omnivores who just like to use a little bit of everything.
Making the jump
It's possible to use the Nexus phones without cellular connectivity, just using them around the house on Wi-Fi or tethering them to your iPhone when you're out and about. To simplify things and cut down on the number of items to carry around, though, I usually just pop my SIM card out of my iPhone and into the Nexus. If you've never done this before, it's not a difficult process. You'll need some equipment depending on what kind of iPhone you're using.