I would choose the Lumia 1020 because of many factors, but I'll state just a few here:
It's got 36 months full support, then a new version comes out and the support time resets. I've also got used to it in this period of 2 and a half years of usage and I wouldn't swap it for nothing. I'm a bit of a smooth flow and no-lag experience, I'd constantly lose my mind if that would happen on another phone. Security is.. Hm, I can say without any hesitation flawless, because I haven't noticed any major breakthrough in the hacking of information out of Windows Phones. So I would say that it's a pretty safe OS. And the updates are from OEM to OEM different, HTC almost never updates their phones, I won't even talk about Samsung, and Nokia is doing a great job, they're even adding features to the OS that no other OEM has, nor has ever tried to do that. Don't know if they haven't had the option to do so, or they were too busy with their other flagships.
I'd not choose iPhone because of the iOS, the nonstop static gridded icons with just a circle with a number on top of it - nope, that doesn't turn the switch for me. Well, I must admit, I like the design, but neither that doesn't do for me. Software matters a lot for me. Apple has a decently secure OS, with almost no significant security breaches that are publicly known or are/were notorious because of their significance (except for the lock screen bypass that was discovered a few months ago). The updates are nice and organized, almost no cluttered or messy fragmentation as it's seen at Android (sorry Android Central people, but it's unfortunately a bit/a lot true, your decision).
Galaxy S4, well, here we go with the beast.. I know that it's powerful as a behemoth, but there's my software part showing itself again - the Android doesn't pull the trigger for me. I've seen too much news about security breaches about Android, and I'm a little paranoid about them, so that's the first no. I also don't like the customization Samsung provides, neither the system itself. I know, I could flash any other ROM on it and enjo it to the max, but I don't like to play with m phone in such a way that I could break something (warranty, possibly brick, and so on). Linux never worked for me, sorry Linus, hehe. And also a major factor is because Samsung (that isn't pointed only on that OEM, it applies also on many others) don't provide their phones with updates also months after they're officially released. Some phones are also "forgotten" in the vast amount of new devices, which are coming out almost on a daily basis, and that creates an insane fragmentation rate.
My decision goes to the Lumia 1020, and sorry for the long post
