Not sure if any custom ROM has the latest from the S4, however, some ROM developers have pulled in certain features and made them available as part of the ROM, or as user installable zip files. The ROM based features can be in some cases, selected during the ROM installation phase.
There are many TouchWiz based custom ROMs out there. A few that I'm aware of are CleanROM, Jelly Beans, and MeanBean. I personally use CleanROM as its close to stock, and the developer (Scott) and his team are great at helping beginner and advanced users alike. I read good things about the other ROMs and their developers that I listed, and believe there are likely even more good ones for North American carriers. As for the International custom ROMs, that's where my knowledge base stops.
For non-TouchWiz, there are some based on Android 4.2. Cyanogen, and Carbon are just a few.
To learn more about either custom ROM variant, here are a few links to help:
Scott's ROMS - Home
RootzWiki
Verizon Galaxy Note II Android Development - xda-developers