After using this for a few weeks I just wanted to report my experience using it with the Note 3.
My brother has the similar Belkin kit and it is absolutely TERRIBLE. It flashes red and refuses to connect to anything for days at a time then seemingly works for a month or two, the speakerphone is absolutely unusable, the precise timing required to use the ONE button for Play, Pause, and Next Track is maddeningly difficult (leaves you blindly wondering if it is paused, resumed, or skipped), and it is simply too expensive.
I am happy to say that I didn't have any of those issues with the Kinivo kit. It sticks with a double-sided sticky foam disc instead of the two-part magnetic base that the Belkin uses but I don't plan to move it around and it's not like Belkin included two bases anyway. With it stuck solidly on the dash, I kinda wish it had a twist to skip function but the dedicated buttons are certainly good enough for that! The wireless connection is solid and the controls feel/work great. I have no idea if it is using Apt-X or not but it supposedly supports it for higher-quality A2DP streaming over Bluetooth (as does the Note 3). The quality sounds much better but that could just be my car having better speakers compared to my brother (I am no audiophile).
Unlike the Belkin, it auto-connects when you start the car. That would be fine if it didn't cause the phone to also auto-answer! Further compounding it is the fact that it comes on even when your stereo is off so you may have no idea that it grabbed the call (you can't hear the caller without powering on and switching inputs). Obviously, there's no easy way for them to integrate with your OEM stereo to only operate when the stereo is on and AUX input is selected, which is the drawback to having an adapter kit. I don't know if the auto-answering is bad behavior on Samsung's part or if it does that with every phone so I'll have to test. There have been times leaving work with my ringer silenced when it would answer a call I didn't even know was incoming and then I drive around completely unaware that someone can hear everything going on in the car. Galaxy Charging Light reports 1800mAH charge rate through the built-in USB port, which is as fast a my phone charges from the stock 2-amp wall plug, but I do wish it had a second USB port or was de-coupled so that you could bring your own. The Belkin does have a smaller plug but they both occupy the whole power socket, they both only have one available USB port, and they both are permanently wired for their own power.
Speakerphone is a million times better than the crappy Belkin unit. I'd barely be exaggerating to say that the Belkin is completely unusable for phone calls while driving. This actually WORKS. I am somewhat hard of hearing which is why I'm no audiophile, but this was perfectly adequate.
There is no battery and thus no need to charge it. It really came down to the Belkin and Kinivo for me purely because I didn't want one of those rechargeable units. A significant number of users reported feedback issues when charging in many vehicles and I don't want to deal with worn batteries. While I can't confirm that wired units are immune to this, I didn't have that issue in my 2011 Corolla or my brother's 2009 Aveo. People act like you just have to suck it up and buy the fix (ground loop isolator) if you have this problem but I ask "why can't it be built-in?" If possible, I expect that.
I hope I can fix the auto-answer problem with an Xposed tweak or something. All in all, I am very happy with it and I want to make sure none of you waste your money on the terrible Belkin version! I decided on this back when it and the Belkin kit were the only two similar options but I see a new "iClever" Bluetooth 4.0 kit has showed up on the market. It costs less, includes a dual-port charger (occupies one port but at least it's de-coupled so you can BYO), doesn't mention Apt-X,
but I'd love to hear from anyone with experience with it.
Kinivo BTC450 kit:
iClever Himbox HB01 kit: