I've had the orange one for nearly a month now, so slightly more than initial observations.
1. Looks - it is very neat, and I like the "burnt orange" colour. Had plenty of positive comments about the looks - a bit different and eye-catching but still smart. The form factor is perfect for me. I've had big phones, but I like the more compact size for now.
2. The famed battery life. Well, to be honest, I haven't played much with the settings. It comfortably lasts all day - using between 50% and 75% by the time I get home in the evening. Yesterday was a heavy day - I listened to Spotify for 4 hours (using Aptx bluetooth headphones), 1/2 hour of streamed video, 1/2 hour phone calls, 1/2 hour of sat nav use, some testing on some apps we are developing, and the usual emails/texts etc. When I looked at the battery usage when I got home I'd used 75%. with a screen on time of 4 hours. Factoring in the fact that the signal is pretty poor where I work, so the radio has to work hard to maintain a signal, I think that is not bad. I might mess around with the stamina mode when I have time, just out of interest, but the phone is good for day-to-day usage.
3. Screen. It is lovely. Now. Out of the box it was far too cold for my liking. A quick adjustment of the white balance (R98 G121 B0) and making sure Super vivid was off (but X-Reality was on) and it is vivid but reasonably realistic. Viewing angles seem fine - Sony has had issues with this in the past, and the Z3C isn't as good as some others, but is good enough for me. 720p is absolutely fine at this screen size IMO.
4. Sound. I don't use the speakers much, listening to most things through headphones, but they seemed OK. Loud enough, but not much more. Via headphones, the Z3C sounds great, and I don't have any problems with gapless playback, both Spotify and Google Play Music seem to support it fine. Call quality is good, but not fantastic.
5. Connectivity. My impression is that the wifi reception isn't the strongest. Other people at work seem to have more reliable connections to our dodgy router than me. 2G/3G is very decent, however, considering how poor Vodafone are in the UK outside of cities. Much better than my previous Samsung and on a par with my Nokia. Bluetooth seems strong and reliable.
6. Camera. Seems OK. I have been using a Lumia 1020 and the Z3C struggles in comparison. It fires up quickly (which was a real problem with the Lumia) and the photos are reasonably detailed, and it performs OK in poor light, but there is a lot of noise at times. I haven't really fiddled about with the settings much yet though, so perhaps I can improve things when I have time. I've been using the camera on manual mode in the main.
To conclude - I am pleased with the Xperia Z3C and can see myself keeping it for a year at least. It is a fast, good looking and enjoyable phone to use, and Sony's decision to put almost top of the range components into a smaller chassis means that, for me, it is close to being the ideal phone.