I've been a fan of the bigger sized phones for some time and Samsung has been paving the way in terms of quality large phones. I remember when I had the 4.5in screened Samsung Infuse and it was considered large. I've had a Note and Note 2 and loved both. Note 3 continues the tradition of keeping everything that worked, improving where needed, and adding features I wouldn't have even thought to ask. So many of the little annoyances I had with my Note 2 have been addressed. Its clear they put a lot of thought into finding out what people loved and wanted changed.
When I first held the phone I fell in love. The form factor is just great and the screen is a noticeable jump up. That's saying something when the Note 2 already had a stellar screen resolution. I don't feel the need to have this one in a case. The slippery back of the Note 2 required a case as I dropped it a couple times when holding it bare.
Rather than go on feature by feature I'll suffice to say everything feels like a great and noticeable improvement. S-pen, camera, screen, on and on its the phone I loved before but better in every way I could have asked for. I've tried dozens of smartphones over the past 5 years. The Note 2 was the first one I actually held onto for a year. I easily see myself holding onto the 3 that much or longer (depending on when they bring out a 4th ;) ).
I highly recommend this phone.