IPhone 5S vs Note 3 and HTC one?

I'm looking into getting a new phone. I can't decide which I want though. I currently have the HTC one and I like everything except for the fact that I can't send videos. The videos have to be no more than 5 seconds and have very low quality in order to be sent. My family lives 3 hours away and I send videos daily of my daughter. (This is why I'm considering the iPhone 5S) I had the iPhone 5 and could send videos as long as I wanted. What is your opinion? How is the Note 3 compared to the iPhone 5S and the HTC One for that matter.

Added (1). I'm using the camera app that is installed. When I chatted HTC they said I had to set the quality to MMS (176 x144). Any time i've tried sending them longer than 5 seconds, it makes me 'Edit' the video.

I got 5S and I'm really glad I made that decision

I suggest you buy galaxy note 3 it, s have a lot of features
Brand - Samsung.
Model - Galaxy Note 3.
OS - Android OS v4.3.
CPU - Quad-Core 2.2 GHz.
GPU - Adreno 330.
RAM - 3 GB.
Display - 5.7 inches Super AMOLED Touchscreen.
Camera - 13 MP.
and more features so you can buy it

What app are you using to record/send these 5-second videos? Android phones, including the HTC One, can definitely send videos longer than 5 seconds. It sounds like maybe you're using Vine to record the videos, which, if true, would be the source of your problem. Vine, by definition, records only very short videos (though I thought it was up to 15 seconds).

Another problem might be *how* you're sending them. Are you sending them via MMS, or with an app? You can send long videos in Android using WhatsApp or Kik. You can video chat (rather than recording and sending a video) using Skype or Tango or Google Hangouts.

In any case, your 5-second video problem isn't because of your phone.

As for a new phone, if you've already purchased apps and are used to Android, between the iPhone 5S and the Note 3, I'd recommend the Note 3.It's larger, has a higher-resolution display, and features expandable storage for all those videos via a microSD card slot. It also has a removable/replaceable battery.

Hope that helps!

Here is a sample of the HTC One's HD video capability, showing (a) video much longer than 5 seconds and (b) very high-quality video, unlike what you're somehow getting…

Good luck!

UPDATE: OK, so the problem is that you're sending these videos via MMS, which really isn't designed for long or high-quality video. Changing phones will NOT change that situation. If you want to send longer videos, I'd recommend that you and the person/people you're sending the videos to get Kik Messenger. Here are links to Kik for Android and Kik for iOS, both free:

Kik Messenger for Android:
https://play.google.com/...ik.android

Video sending helper app for Kik Messenger (Android):
https://play.google.com/...yvideo.kik

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Kik Messenger for iOS:
https://itunes.apple.com/...18860?mt=8

Video for Kik for iOS:
https://itunes.apple.com/...95062?mt=8

Hope that resolves your issue!

UPDATE 2: Another way to send videos to people would be to record your videos and upload them to YouTube, then share a link to the video with your family and/or friends. There are privacy controls on YouTube that allow you to limit who can see your videos. The YouTube app for Android makes the process easy.

Get the iPhone 5S. You won't regret. If you need iPhone 5S without contract or unlocked cheaper than retail, mail me.