The Note 3 has a huge full HD screen, a quad core 2.3GHz processor, and 3gb of RAM. Most people don't have computers with those specs.
I'd highly recommend handling one in person. It's not just a beast of a device in terms of specs, it's also a beast in size. Really, this thing is huge. That's both a good thing and a bad thing, depending on how you look at it, and how much pocket space you're looking to devote to your phone. If you can't tolerate the extreme size, the Galaxy S4 is worth looking at too. It's no slouch in the hardware department, has a wonderful screen (and if 5" is too small, then maybe there's something wrong with you), and is actually smaller all-around than the S3.
Samsung has a massive marketshare in the mobile device market, dwarfing all other manufacturers except Apple, and it's not by mistake. Their devices are all cutting-edge, and they're great with keeping them updated with newer versions of Android (unlike so many other manufacturers). Samsung also does most of their competitors better in several specifics; these days many phones have sealed batteries and lack storage expansion via micro SD cards, but Samsung still keeps their batteries changeable and gives you the option for a micro SD slot. Their phones don't exactly exude a premium feel with their plastic construction, but IMO this is mostly irrelevant, or at least it would be to me, since if you're going to spend that much money on a phone, you should have it in a protective case of some sort.
My contract is up in April, and I'm definitely considering getting a Note 3 myself, although 6 months from now there may be something else to consider. For me, my phone is barely a phone. Instead of being a phone with computer-like capabilities, my "phone" is more like a pocket computer that I can also make phone calls with.
