IPhone 5 vs HTC One vs Samsung galaxy s4?

So my mom wants a phone that does really good for taking videos with the camera. Now I have the iPhone 5 so she wants a different phone, either the HTC one or the Samsung galaxy s4. She wants to know which quality is on par with the iPhone 5's quality. Ex. I can take a good sounding quality video of a band and it sounds pretty good and clean. My old HTC Evo 4g couldn't even take a video of a band playing without sounding really bad. So my question is. Which of the two, the HTC one or the Samsung galaxy s4 is the best at taking good quality videos like the iPhone 5?

Samsung all the way.

Iphone

There's a samsung galaxy s4?

Samsung galaxy s4 has a much better camera than the iPhone 5 so tell her to get that

Personally I believe that the Samsung Galaxy S4 is better because
1.It is quicker- 1.9ghz quad core vs 1.7ghz quad core

2.Microsd- you can expand the memory with a 64gb microsd. This a cheaper way to expand your memory and you can have a 16 gb S4 and still have more storage than the HTC One(64gb) if you get a 64gb microsd.

3.Removable battery- This means you can replace the battery if you run out of charge when you are around unlike the HTC One which you have to charge or bring an external charger and charge it from there, however this is an akward way of charging your phone. Also the removable battery can help you prevent water damage as you can remove the battery if it falls in water, thus reducing the chances of water damage.

4.Repairability- iFixit gave HTC One the worst rating for repairability and gave one of the best to the S4( http://www.appy-geek.com/Web/ArticleMobile.aspx?regionid=4&articleid=8679015)

5. Screen- It is amazing and bigger than the screen on the HTC One (yes this is an advantage). Yes it has less ppi (440ppi S4 vs 468ppi HTC One) reviewers say that the difference in ppi is unnoticeable but you can see the difference in colours as the amoled display is has amazing colours and blacks are black (unlike LCD). The big screen is also an advantage as it as you can do so much more with it, multitask for example. Size wise even though the S4 has a screen.3 inches bigger the two phones are around tge same size so for one handed use neither will be different

6. Real Multitasking- watch videos while online, write an email while watching a video, send a message while surfing the web, you can split the screen in two so you can multitask without a bother, this can't be done on the HTC One.

Hope this helped

7. Samsung added features

a.Smartstay- won't turn the screen off if you are still looking at it.
b.Smartpause- pauses a video when you turn around and turns it back on when you turn back
c.Eye controlled webpage scrolling
d. Airview- check link to learn more http://www.phonearena.com/news/Samsung-Galaxy-S-4-display-Air-View-and-Air-Gesture-demoed-on-video_id40881
e.Infrared TV remote(on One too)
f.External temperature and humidity sensors
g.Use the phone while using gloves
h. S Health- useful for health enthusiasts
i. S Translator- it's all in the name a translator
j.Etc- I could go on but check the link to see even more features http://www.phonearena.com/news/Samsung-Galaxy-S4-10-exclusive-or-little-known-features-review_id41541

8.Camera features- First of all reviewers say the only place that the HTC One beats S4 camera wise is in low light without flash. However for the rest the S4 wins, more detail in pictures better videos.
( http://au.businessinsider.com/htc-one-galaxy-s4-iphone-5-camera-test-2013-4) Plus with all the features it's an even better camera

a.Dual shot- take photos from both cameras so that you can include the photographer in a photo
b.Photo with audio message- record a message before or after a photo to add to a photo
c.Eraser shot- can remove unwanted moving content
d.More but those are my favorite

9. People say the metal feels premium, personally I have used both HTC One and S4 and have found that the feeling is different, the S4 does not feel like a cold metal brick in your hand but feels strong and sturdy yet not cold. Plus if you like metal but use cases you won't notice any difference as the cases are virtually all plastic.

10. For gamers, the S4 has the quickest gaming graphics on any smartphone so you won't have problems while playing games (http://m.cnet.com/news/samsung-galaxy-s4-has-the-fastest-gaming-graphics-of-any-phone/57581021)