At this point in time, almost all high-end phones work really well (note 3, iphone 5s, HTC One, Xperia Z1s, Nexus 5, etc).
Thus, you should pick a phone based on your needs.
If you use your smartphone as more than a phone (lots of reading, video, browsing internet, playing games, etc), then get either a Galaxy Note 3 or LG G2. They have excellent battery life, great and spacious screens for media consumption, and good cameras.
If you use your smartphone mostly for texting, social media, and making phone calls, the iPhone 5s would be the best pick. You also get one-handed usage from the iPhone, a plus if you're not comfortable with the size of larger smartphones. The iPhone has a pretty good camera too. Ah, and people love Apple's warranty support.
If you need a waterproof phone (for those that like to take their phones into the shower/bath... >_>; ), then a Xperia Z1s or Xperia Z compact are good choices. Choose the compact if you want one-handed usage.
For the HTC One, you should choose it if you want a beautiful phone. It's camera is lackluster, but everything else about it is gorgeous from a hardware standpoint.
And finally, if you are on a budget and want a phone that's reasonably good on all counts, choose the Nexus 5. The Nexus 5, with it's 5-inch screen, is easier to handle than the Galaxy Note 3. It's large enough to make media consumption easier than the iPhone, and it handles texting, social media, and phone calls quite well. As an added bonus, you get prompt Android updates from Google when they're released. On the downside, LG has been having quality control issues with the Nexus 5, resulting in some batches having audio recording issues.
On a side note, a Windows phone might be a decent choice, but beware of the lack of apps in the app store. But if you can get over that, the Lumia 1020 has the overall best smartphone camera, period. There is no camera currently better amongst smartphones.