I have had my Note 2 for a couple of weeks. It is an excellent phone, game unit and media consumption device. I pretty much like everything about it.
First it is not as big as you think it is. The sites that complain about that appear to have not taken the time to really use the device. Yes, it is bigger than pretty much any other phone out there but not 2x the size.
Second the battery life has been wonderful. Charge it every other day if you don't play a pile of games. I don't do that much calling or get very many texts so it is generally not busy doing much. It has never left me in the weeds for battery needs.
I am using Llama on the phone so it knows when I am at work turning off WiFi (they don't have it at my job which is another issue) and turning down the main speaker sound. At home it cranks up the sound so I can hear it in the house when I lay it down someplace and it connects to my WiFi. I have the sound muted at night. Works like a champ and is a great free program.
For games this is a perfect size. I have a Xoom tablet where I played most of my games in the past as the phone was too small. Not anymore. This really is a great gaming size. I have pretty much normal sized hands, not little lady hands or big basketball player hands. I would say just average for at 6 foot tall person. The games I have played seem to work the best on this phone over any other device I have used. Everything is in reach and the touch zones are the right size.
For IM this phone is awesome. I get to use Swype when I want or pull out the stylus and write. The hand writing recognition has been spot on. Nice job Samsung. Using Swype on this size of device is so much easier. Even just typing each letter works great. Keyboard is the right size and having the numeric entry area above the alpha part is super handy. I always need to type a number and not needing to switch keyboard layout is darn handy.
I have used the paint program to draw various things including screen wire frames for work. The stylus is very responsive. I need to practice my drawing skills and having this device in my pocket at all times is pushing me to do that. I don't find the stylus to be a gimmick.
The Calendar app is very usable. My wife and I have our shared calendars along with those of the kids and their school activities. Having the snap shot calendar widget on my home screen is super helpful and then using the Calendar app to dig into details or look farther into the future is really easy.
Web browsing shines on this thing in landscape mode. I generally request all pages as desktop pages. Landscape gives the proper width and font size to make it all very easy to use. Thanks to Google and Chrome and I have my bookmarks linked. I can quickly check out action on my favorite sites. Searching is easy with the various entry flavors.
I have used the dual screen mode. I don't use it often but when I need it the ability to have two apps open it is awesome. I was doing some research and needed to copy URLs from the browser to an email. I split the screen and had Chrome and GMail open at the same time. I sized them for Chrome to be 75% of the screen and could quickly copy and paste the links right into the email. This rocks! Sure I will find other uses for it too.
I don't feel I have figured out as many of the cool features as I could use on this device. I am working as a contractor so my time has been dedicated to that area right now. I am trying to scan more Note related websites to pick up new tips. So much of what this thing can do is a mystery and I want to learn all the short cuts and cool features to get the most out of it.
Really people, go to your provider and give this phone a shot. It really takes the smart phones paradigm to a new level. It has replaced my need to grab the tablet when I am at home. I type more and do more everyday. Heck I hardly fire up my desktop anymore expect to type in something super long such as this post.
I have to use the iPhone at work as a comparison device as I am writing the Android version of our software. That phone feels so tiny in my hand. My fingers want to wrap around it and hide the screen. Everything about it is tiny. You can barely see anything on a web page. Books have pitiful amounts of text. A map barely shows any farther than you can throw a rock with any sort of detail. Each screen has just a snippet of information on it. I can't go back to that size of phone for sure.