Should i buy the note 3 or keep my iPhone 5s?

I have an iPhone 5s 64gb and I'm bored with it. I want to be able to multitask and use my phone as a remote and have a bigger screen. But me and my long distance relationship girlfriend both have iPhones and we use iMessage and FaceTime. So she's mad because i want the note 3 and we won't be able to FaceTime or iMessage but i tell her android has apps that are similar. She mad because i want to switch what should i do? We text all the time and FaceTime like 6 days a week. What should i do please help?

Tell her too bad, android is better and switch.

If you are bored already then nothing in life will make you happy, you are just one of those who is always bored.

Note 3 is a much better phone.
It is much more advanced.
Has better specs.
Better screen. Even with and extra 1.5" it's still sharper than any Iphone.
Android beat ios hands down.

You should keep your Iphone 5s, cause the note 3 is too uncomfortable to carry around. The size difference can be seen here

Ignore anyone who says that one is better than the other, because they are wrong. The truth, is they are both geared toward different audiences, and both do what they are intended to do very well. I will explain the uses and merits of both.

Android:
-Designed for users who enjoy theming and customizing, and don't mind getting their hands dirty
-Good for heavy Google users

Pros:
-Extreme customizability
-Google integration
-Most (not all) phones have removable storage and battery

Cons:
-Occasional instability (and I mean occasional, it doesn't happen too much, and improves with every update)
-OS fragmentation, meaning that updates can take forever or never arrive
-Lots of choices of phones clamoring for your attention
-Bloatware basically everywhere

iOS:
-Good for users who don't want to get into the nitty-gritty of a phone and just want something that does the basics without too much effort

Pros:
-Little to no fragmentation, meaning quick updates
-Easy to pick which phone you want
-More stability
-Easy to use

Cons:
-Very little customizability (meaning basically none)

That's the general gist of it. Next, an explanation of how things work if you are willing to go outside of the OS's restrictions.

Android:
Rooting is the way to escape Android's limitations. It gives you basically unchecked access to the phone, Really only for serious power users. To do it, you have to do most of it yourself, but everything is on your terms.

Pros:
-Do basically whatever you want
-Removes bloatware

Cons:
-If you don't know what you're doing, you can mess up your phone pretty badly

iOS:
Jailbreaking is iOS's way to break free and has a massive, united community. It's much simpler to do, with tools like evasi0n. The problem is, it's extremely hard to make, and often takes months to develop (like right now). This means that you will often be stuck between updating and losing your precious jailbreak or keeping an older version of iOS.

Pros:
-Gives you lots of ways to customize and tweak your phone
-Huge, active community (just check reddit.com/r/jailbreak)
-Lots of tweaks with almost constant support
-Once it comes out, it's as easy as pressing a button labeled "jailbreak".
-Basically impossible to permanently mess up your phone

Cons:
-Can't give you the complete control that rooting does
-Can take months to develop
-May leave you stranded on an older version of iOS

This is my complete analysis. I leave it up to you to decide.
If you have already invested in one ecosystem over another, I strongly suggest sticking with it.

Just keep your iPhone 5S.

I think your girlfriend is right. But you judge on what you want. Note 3 is the best phone in the market. If you like a big screen, sony xperia ultra has the largest screen of all phones. And you can use it like a remote too.

Keep your iPhone 5S and find some interesting apps and games on the App Store. Honestly, it isn't that hard!

Apple all the way bro!

Buy Note 3, It's an enjoyment on Note 3 to watch videos, play game, browse webs…