I think I can add something useful to this discussion. I was in the same boat as you, Matt. I was a longtime iPhone user who always found myself curious about the developments in the Android world. I followed the progress as each new major release became more appealing. With Lollipop last year, I thought finally they had reached the tipping point. I was really taken with everything about Lollipop. The look, the functionality - it all seemed so streamlined and refreshing compared to iOS. I couldn't resist trying it.
I picked up a Nexus 6 and split my usage between it and my iPhone 6. I can't deny that there is a lot to like about Android. After using it a while, the one feature I value more than any other is the true multitasking. I didn't know what this meant until I used the Nexus for myself on a daily basis. What it means in practice is that I can have music playing from one app, then open another app with audio capability, and my music doesn't get cut off. Then, if I choose to play something in the second app, the audio output will switch accordingly. In my notification drop-down I will then have audio controls for both apps, and I can switch between them at will by pressing their respective play buttons. Of course this also works with more than two audio apps at once; basically any recently used audio stream will show playback controls in the notifications, for easy access and switching.
To contrast this with iOS, if I'm playing something in the Music app on my iPhone, and then switch to the Podcasts app, only to look at available podcasts or see what the latest episodes are, my music stops playing. And I've found this to be the case whenever I switch from one audio app of any kind to another; the playing audio stream stops immediately when another app with audio capability is opened. It doesn't matter that I didn't actually want to play anything from the second app. This is the one-thing-at-a-time limitation of iOS, I guess.
Another instance where I've noticed the value of the multitasking capability is when running multiplayer Minecraft. If I'm running it on my iPhone, and the other players have joined my world, everyone gets kicked out of the game if my phone needs to do something else, like answer a call or reply to a text. This can get rather irritating very quickly with multiple interruptions. With the Nexus, on the other hand, I can start the game and then use my phone for anything else at all without interrupting the game for the other players. It's quite nice.
For me, Android's multitasking has turned out to be its greatest strength, and its greatest advantage over iOS. And it's not something that I thought about until I actually used an Android phone on a daily basis for myself. It wasn't on my list of reasons for wanting to try Lollipop, but now it is at the top of my list.
I will repeat what others have said. Don't even consider anything but stock Android. That means, basically, a Nexus or a Motorola, at this point. Google's current system of leaving it up to device manufacturers and wireless carriers to update non-Nexus phones with essential security updates, etc., is a sad, sorry joke. The fact is, they don't get updated, unless you're one of the lucky few.
Now, with all the positive things I've said about my experience with the Nexus 6, I still find myself using my iPhone 6 more often, and for longer periods. With all its limitations, it is still the one that least irritates me. I thought Lollipop would finally be the fully baked Android we were waiting for, but the fact is that I've found it to be rather buggy, even on a fully stock, non-rooted Nexus 6. Google's own apps crash regularly for no apparent reason. I often find the display hot to the touch when I'm doing nothing with the phone except browsing the web with Chrome. And I mean it's so hot that it is unpleasant to place my finger on it to scroll the page. I have no explanation for it, and it comes and goes randomly. At times, it runs nice and cool, and other times it's a hot plate. In both cases, nothing besides Chrome is running.
For all the aesthetic advances Google made with Lollipop, it is still rather unattractive in many aspects of the OS, and in Google's own apps. I don't like the use of one dominant color to identify one app from another. For example, Google Play Music is a sea of orange. It's an orange dream for anyone who is crazy about the color, but what about the rest of us? And they don't use tasteful little accent colors here and there; they just splash the color over the whole app in buckets. The YouTube app hurts my eyes because of the intense, huge blocks of red everywhere. If you want to use Hangouts, you better like the color green, and I mean you better REALLY like it.
As a general rule, all the major Google apps (Maps, YouTube, Gmail, Hangouts, Drive, etc.) look worlds better on iOS; they have far more tasteful designs. And I've even found them to work more smoothly and with less hiccups. That's true of just about everything on iOS when compared to Android. In my experience, Google still has a long way to go to match the buttery smooth experience of using an iPhone.
Yes, there are limitations with multitasking, and you have to put up with Apple's way of doing things, but the overall experience on iPhone is the one I keep coming back to.