Best phone for the money huh? This may sound like a broken record, but have you considered an iPhone? IMO, there is a reason the Android GUI is similar to that of the iOS

Just saying.
iOS sucks for power users in my opinion.
Its simple and easy to use, but lacks so much. iTunes sucks. Multi-tasking sucks. You can't even play a MKV or any popular format without screwing around with so many things like jailbreaking, etc. My opinion anyways.
OP:
Jelly Bean is so smooth and fluid and offers so much more with customizing, tweaks, etc out of the box. Much more codec support. 720p and 1080p Screens.
If your like me, Custom Roms then add so much more to an already great base. I'm using the Viper 2.0 JB rom on my One S (A great phone on its own) and its awesome.
I think you should add the HTC One X (S4 version) or X+ (Tegra 3 1.7 GHz) on your list too. (The One X+ Tegra 3 outperforms the One X Tegra 3 1.5Ghz but quite a bit so I'd take it out of the mix) Latter has 64GB storage built in, runs Jelly Bean, and both have the nicest 720p screen on the market. The One X and One S also have super nice cameras (better than Nexus 4/Optimus G for sure). There are hacks to allow 1080p 40Mbit video and uncompressed JPEG images too. (both built into Viper Roms) HTC also has a good track record recently for updates. HTC sense (4 or 4+) is also very fluid and easily the best skin on a phone in my opinion. The S4 version has excellent battery life and feels equally snappy, but has 16GB storage rather than 64GB. The Tegra 3 version's battery life is not as good as the S4 version though.
The Optimus G is a beast. It has a really nice screen too (still think the One X is better) but comes with ICS out of the box. Still, its probably the snappiest phone currently available even on ICS. LG did a WONDERFUL job optimizing that Rom. I believe JB is already available too. The Camera's are not as good as Samsungs or HTC's top tier phones. (Even the 13MP is worse than the HTC/Samsung 8MP Camera. Sony's 13MP Camera is also worse than HTC/Samsungs 8MP Camera, so MP isn't everything).
The Nexus 4 is basically an Optimus G with less storage and Jelly Bean 4.2. It's a very nice phone. It's camera is disappointing but definitely does the trick for most people. I bought one from Google and had for 3-4 days, but decided to Ebay it for the money. I liked the phone overall.
The Note II is probably the best all around phone if you like big screens, although I'm not a fan of Samsung's build quality. (Plastics are flimsy). I also generally prefer LCD screens over AMOLED even though my current phone has the AMOLED (which I consider its weak point). Some people love them though. It's fast, has good developer support, LTE and a good camera. Has SD support with exFat out of the box. It also has excellent battery life.
I agree, there is a lot to chose from. The 4X is a nice phone too. The Video has been fixed, and its also very snappy. I think the Camera on the 4x takes better pics than the Optimus G for some reason. LG's screens are underated. They use IPS LCD's with very nice quality. They are bright as well. Only negative is no JB update announced yet, which is LG's flaw. They are late on upgrades but promise the Optimus G will have quicker turnarounds.
Lots to chose from. The Motorola Razr HD Maxx is a very nice phone too. It's camera is not as good as HTC or Samsung, but it has top tier battery life and top tier build quality. Motorola is owned by Google so expect faster upgrades now. (it's already on Jelly bean). Motorola's new phones are very close to stock Android too if thats your thing.
Quad cores are nice, but any phone with the S4/Adreno 225 is going to feel just as snappy.
The One S is a very nice phone too, but I'm biased. I repair phones and flip them on the side, so I've hand my hands on almost any phone out there. If you can live with qHD and 16GB, I think its the most comfortable in hand phone I've ever used, and it's flawless and fast.