I have a Nexus 5, and I purchased a Note 3 for $380AUD a few days ago with the intention of selling it on Ebay for $600. After playing around with it the last few days, my girlfriend has decided she wants to keep my Nexus 5, so I'll keep the Note 3. Honestly though, other than the bigger battery, it feels like a bit of a side-grade. That being said, I can get 6+ hours easily of SOT, with an hour or so of heavy gaming. If I was to just browse the web, check emails and listen to music, I'd get 7.5 to 8 hours. I love the feel, look and concept of the Nexus 5, so I really wanted to keep that, but the Note 3 is still pleasant to use. The longer battery life is certainly welcome. The size is a bit ridiculous though. I'm used to being able to operate my Nexus 5 one-handed, whereas that isn't possible with the Note 3. I'm not a small guy either. I'm 6'2 and have pretty large hands.
All in all, if you can get a Note 3 for the price that you could sell your Nexus 5, it might be worth it. I certainly wouldn't purchase one for any more than that though, as you'll find it offers diminishing returns for the cost.
Nexus 7 (2013)
32GB Flo stock ROM and rooted
Nexus 5 "Stormtrooper"
32GB stock ROM/Franco Kernel and rooted
Motorola Xoom Z604
32GB running My Android 4.2.2 (Sold)
Galaxy Note N7000
16GB running SweetROM V9 (Given to Mum )
Huawei Ascend Mate
8GB stock ROM and rooted (Sold)
running SlimBean 4.1.1 (Unused)