Another new to Android/GN3 owner here.
I've had it for about 2 weeks now and I am loving it! I too came from the iPhone 4s. Been an iPhone user since the 3G, and until recently, you would have found me singing the praises of the iPhone. Admittedly, I was pretty much in the dark about Android, so there was a bit of that "fear of the unknown."
I was pretty happy with my 4s, but only because I have been a jailbreaker since my first iPhone. It was the only way I could enjoy the phone the way I wanted. But of course, with every new iOS update(especially major ones), meant having to wait a long time for a new jailbreak, or lose the features that I had gotten so used to. Even now, there is still no jailbreak for iOS7.
There's also the issue of screen size. I've always felt that the iPhone could increase its screen size, or offer a larger version. When the 5 came out, I was pretty disappointed that they just stretched it out a bit. Still looks weird to me. Who knows if they will ever go big. It seems to be against their ideology.
The coup de gras for me was iOS7 itself. I just don't like the changes. Maybe waiting for a jailbreak would allow for customization to my liking. Maybe not. So all those things combined made me take a real close look at Android.
At first, I was looking at the S4. A nice looking phone with a substantially bigger screen than the 4s. I was aware of the Note 2 and pretty much wrote it off as being ridiculously big for a phone. Then a coworker shows up with the Note 3. Sure, at first glance it did seem absurdly big, but then I started holding it for a bit, putting it in my pocket and such. The first thing that really surprised me was the weight. I think my brain had a hard time grasping that a device this big could feel so light.

My coworker started showing me a bunch of the cool features and how the s-pen works. Right then and there, I was sold.
So, two weeks in now and I'm still adjusting to it a bit. Not necessarily the size of it, which I now think is pretty much perfect, but the ins and outs of the OS. I had to get some info off my 4s the other day and it felt like holding a pack of gum, lol. I still get a bit giddy when I show people that the 4s can fit completely within the screen space of the Note 3.

My eyes love me for it as well. I'm pretty near sighted and I was starting to struggle a bit to read text on my iPhone without taking off my glasses. Don't have that problem with the Note 3, no sir.
Making the switch hasn't been without a few quirks and sacrifices. The first thing that bewildered me was the lack of built-in visual voicemail in the phone app like there is on the iPhone. It took me a bit to realize I would have to download an app of my choosing from the play store to get that functionality. I like having things consolidated so it kind of annoys me that I have to have one app for phone, another for voicemail. I decided to go with the AT&T Messages app since it at least combines messages and voicemail. It just seems a bit counterintuitive at the moment, but I'm getting used to it.
Another minor annoyance has to do with the fact that I'm required to use an Exchange email account for work and the security requires a PIN and removal of certain features that I would like to use. Obviously that is not the phone's problem however, on my jailbroken 4s there was an easy way to bypass the security via a simple tweak installed through Cydia. Yes, it was a risk to violate the security, but it has never been an issue in the 5 years I've been using the bypass. I thought for sure there would be a similarly easy way to do this on Android, even if it meant rooting, which I have. But so far a solution escapes me, despite scouring various forums(XDA, etc.) and not finding anything that works. I've even tried a couple mail apps from the play store that will bypass security, but they are either unreliable, or not to my liking. I still have a lot to learn when it comes to tinkering under the hood with Android. It certainly does not seem as straightforward as jailbreaking has been.
If you're still reading this I commend you.

I am always on the search for advice, tips, tricks, whatever when it comes to the Note 3. One area of interest is dealing with some of the bloatware and what is/isn't safe to remove, and how.