What do you miss if you don't mind me asking?
The screen. It's absolutely gorgeous. At 4.7 and 1920 x 1080 resolution it's beautiful and can show much more info at once. The 5s screen is lovely, but feels cramped in comparison.
BlinkFeed: Surprisingly nice aggregator mixing news stories with social network activity
Zoes/Highlights: Zoes are mini videos and when you spend some time taking a series of photos and/or Zoes at a particular time or place it creates Highlights, which stitch together pictures plus Zoes and you can choose themes, e.g. quiet music with slow transitions or more energetic music with faster/jumpier transition. Very nicely done way to review memories from a particular day's activities.
Widgets: Being able to mix app icons with folders with things like lists of recent e-mails or tweets or music app controls all together at one level is very flexible and the HTC One is fast enough to run them without hitching
Customizable keyboards: Swype and/or SwiftKey are both excellent, and while the iPhone's keyboard is quite nice, losing that flexibility is tough.
*Great* speakers for a cell phone
iPhone 5S advantages:
Camera takes better pictures and slow-mo is fun & implemented well
The HTC One is a smooth/fast phone, but the 5s is noticeably smoother and faster
Fingerprint sensor works well and is a nicer feature than I anticipated
Music sounds better on headphones
Multitasking is done better on iOS 7
Google Now may be getting creepy smart, but I have more fun with Siri
I prefer Safari to Chrome or HTC browser on the One
HTC One is a lovely design, but the iPhone is still a notch above IMO
I'm sure I could come up with more in both categories with a bit more thought, but those are what spring to mind first. Both are beautiful phones and delightful to use in many ways.