I had the Note 3, twice. LOVE the note 3. great phone. They are a bit big feeling.
I ended up with the Moto x. the 4.7" screen looks great, the vanilla android has a great clean feel to it. The X from AT&T has Very little carrier bloat ( a Lot less than samsung )
4.4 is just an awesome bonus. the cherry on top.
The moto x hands free, active display, always listening, amazing. The way the phone feels, awesome. ( might be the most comfortable phone ever made)
Battery life gets me thru a day with no issues, I don't even own a car charger. (it may not have AS much battery life as Note 2 tho)
I think the moto x is one of the greatest devices ever made. I work at apple and switched to android thanks to the moto x.
however, you could go S4? slightly smaller with every feature you are used to minus the S-pen. The G2 another good option if you are ok with never getting an update to the OS.
The note 3 is the same size on the outside as your phone but a bigger screen, so I don't think that is a good option. (The note 3 is incredible/awesome tho)
I plan to buy a 2nd moto X cyber monday instead of paying for insurance thru the carrier. $7 x 24 = $168 and if I break screen, lose it, or get it wet that will be another $199 so that will be $367 if something goes wrong. I may as well just buy a 2nd device thru moto maker and get the colors I want. I got the all blk version from AT&T, love it. I had a white moto x and I think the blk one looks better over all.
The best Android phone you can buy | Android Central
Good luck