Within the past year I've had a Nexus 4, Nexus 7, HTC One, and now the Note 3 (originally coming to Android from an Iphone 4). A friend just got the Nexus 5, so I've played with it a bit. I can easily say, for me, the Note 3 is hands down the best out of what's out there right now. Of course though, it's all preference. Before getting the Note, I was always hearing about the horror that was TouchWiz. On my Nexus 4 and 7, I ran Nova Launcher, since I prefer it over stock Jelly Bean. On the HTC One, overall I thought Sense was nice, but still preferred Nova. Since getting the Note, I gotta say, I really like TouchWiz! No, I don't like all the colors, layout and lockscreen is still lacking, but as a whole, I think the functionality is great! I tried Nova and quickly went back. I'm a heavy Exchange user and the stock TouchWiz calendar and especially calendar widget are the best I've come across yet. I've probably blown $30 on email/calendar apps for Exchange functionality and nothing (for me) beats what Samsung is doing. I wish the notification shade was more minimal like HTC Sense or stock, and the lockscreen had more customization, but other than that, I just don't see the hate for TouchWiz. The stock Samsung apps are really good. The S-Pen functionality is in a class of it's own. I'm really liking it and more importantly using it where I thought I never would.
Apple makes a damn nice phone. The 5S is the top pick for anyone who wants a smaller screen and doesn't care about customization (my wife is a perfect example). It's got a great camera and the build quality is well, Apple. If you can live in the IOS paradigm and ecosystem, I'm sure it's a fantastic device. Having had an Iphone 1st gen, 3GS and 4, I can't go back now unless they do something 'ground breaking' again. Even a rumored 5.7" display wouldn't immediately make me go, IOS is just too restrictive. It would have to come with an amazing camera or something else as well.
My picks are (in order):
1. Note 3
2. HTC One
3. Iphone 5s
The LG G2 looks like a solid choice as well, but haven't spent any time with it. Hard to say on the Nexus 5. I wasn't too impressed with the build quality. The camera is really hit and miss. It can take some really decent shots, but absolutely miserable ones as well (the focus is way off a lot and painfully slow). I'm sure much of it can be addressed in software updates, but who knows if or when that'll ever happen. Nothing about KitKat has me saying "I immediately need this" -- it'll just be nice to have in some future update, even if that's 6-8 months out.
It's a good time to be a mobile device geek and it's only going to get better. Find something you like, enjoy it for a couple years, then replace it. That's just the game.