Xperia Z1, Nexus 5 or iPhone 5S?

I am in the market for a new cell phone in Ontario Canada, replacing my old and tired HTC Amaze 4G. I always believe in getting the best when it is something I hope to use for a long time. The cell technology is confusing and the price range is wide but I don't mind spending a few extra dollars for a better phone. Regarding features, of course, fast and reliable connectivity is important both WiFi and via the cell network. I also travel and exchange the SIM in some countries so it must be unlocked. Being able to use the camera for recording information clearly such as labels etc would be useful. Also, if the pictures were reasonably good, then I would not need my compact camera. I do not want a humongous phone, but I like speed, ease of use and quick access to the features. What do you think? Are you good with the technology and can make a recommendation with the pros and cons. Would greatly appreciate your comments.