[Nexus 4 Q&A, Help & Troubleshooting] cg9916:
I have both, and what I can say about the 920 is what I'd say when owning an iPhone too (swapped out a 4s for it): I can handle WP8 & iOS because they're always secondary to Android for me. Exclusively I'd struggle with either, mainly due to lack of apps in WP8, and quite a bit overall in iOS. (The app quality in WP8 isn't poor, it's just the lack of a few are killing me, ie TuneIn - that one damn Swiss station...)

As a second device for me, the Lumia has battery for days - 26h off charger with moderate use the other day and it was at 60% - is built like some concoction designed to protect a tank, and the camera is advanced. Plus it's a simple, well-designed, incredibly smooth, handsome OS which focuses on productivity. And truthfully, for times when I don't need two phones, I often want one I'm inclined to use looking at the screen less - that's the 920. More a tool to the toy, in ways, that is Android for me personally. When I got the 920 I was planning on doing the same as the OP, choosing one, and I went with the 920 initially because I didn't want to be fiddling around with the N4, taking time to flash ROMs, research which kernel is best, figure out why this minor tweak has suddenly borked my entire mobile life, etc, when I'm supposed to be achieving productivity on the level of a respectable member of society. Then I got the N4 in my hands. Phenomenal piece. Not a chance that was going back. When I switch from one to the other, the Lumia feels slow in comparison, almost labored; and that's no slight on it, merely a compliment to the N4's screaming speed. So now it's both.

But in terms of real world use - and I live in a big city - the Lumia gets more day-to-day action for me, in part because I don't have a case for the N4 yet, and I'm terrified of flopping it out of my jacket pocket watching the shards spill across the pavement. I don't baby it, and it's just easier to put somewhere and not worry whether or not the 0.5 degrees of incline is going to send the lubricated glass back hurtling to the floor. I don't worry about the 920. I do about the N4. I also get concerned if I'm out somewhere and the battery is going to die, so I baby the use of my phone under these circumstances; will happen with the N4, won't with the 920. For me, the Lumia sort of ticks a "peace of mind" box. I can throw it in my pocket off the charger and walk out the door, not wondering if it'll last through the night or whether or not it might slap up against something on the subway and shatter, etc.

If it was one or the other and I had both in my hands for a few hours before having to give one back, it'd be no contest: the N4, if my initial concerns about the battery are substantial. I think it's a device of remarkably more potential with a wider variety of uses. However, I think the question to ask is not necessarily which phone is better, but which one best fits your life? People use their devices differently.

For the record, I love having both. Couldn't be happier; what the Nexus 4 gives me - the power, speed, apps, customization, etc. - is complemented perfectly by the 920's strengths - battery, camera, durability, simplicity, LTE, etc. As a pairing of phones, and I've owned a lot of different pairings, this is by far my favorite, and one I'll keep a very long time - which is rare. They're almost the perfect complements in my world. Now if someone could take the best of all these traits and make one single device, they could sell it for four figures on contract and watch the lines on release day stretch counties.