(I apologize for the length!)
I made that switch. First... I really loved that SIII... GREAT phone. I ran Paranoid Android 3.99RC2 on it and it was about as good as it gets. At the time, all the KK ROMs I loaded were pretty unstable... rarely did a day go by that didn't see it boot a couple of times (especially switching between wifi and mobile). I noticed that the Nexus 5 was the new 'reference' phone for most all of the KK roms... and it sold at a killer price... but I was under contract with VZW for another couple of years and the Nexus 5 is sunlight to the vampires at Verizon... so it was a dream... until TMobile announced their Break UP program and the rest is history.
First.. the worries. Storage... I admit I was a little reluctant to give up the expandable storage on my S3. But a few months later, there are a couple of things that pretty much assuaged those fears. First and foremost... T-Mobile has unlimited 4G data plans. That is the great enabler. I had already pushed my music collection to Play Music, but I only used it at my house in fear of of data overage wrath of Verizon.... With unlimited data, I can listen to my hearts content. Secondly, that allows me to not worry about bandwidth and set my pictures and videos to always backup to Google+ Photos. So everything gets backed up on a regular basis... So my music is usually always available, and I have a safe place to store my media long term.... That leaves my storage for ROM downloads...
And while I'd LOOOOVE to have a big partition to store a whole mess of Multi-Rom images, that's just frivilous... don't need it.
Now? I have enough space for a nandroid backup, a secondary multi-rom KK instance, and plenty of space for a ton of pictures.... that's all I need.
Battery usage.... I'm running AOSPAL nightlies with a Franco kernel... I just plugged in my phone... at 25 hours, it was at 40% with 3 hours of on screen time. So no complaints there, it even charges fast.
Performance: OK.... My S3 replaced my sturdy little Galaxy Stellar.... and I loved it. The S3 was responsive and rarely got too chunky. But the Nexus 5 is in an entirely different universe when it comes to performance. Out of the box, it's like butta.... really, it runs smooth as glass and load times are blazing quick. I've had it for over two months now and I am still amazed at how much this phone screws.
Camera: Nexus 5 has a better camera... it's not a DSLR or anything like that, but it takes pretty good pics overall and stunning pics under the right circumstances. The stabilization in the Nexus 5 also works great, unless you've had too much coffee, videos are almost steadi-cam smooth.
Pretty much everything about the phone is superior to the S3 (which, again, I really liked in its own right). Glad I switched.