This is why I went with the note.
First of all the Note has been deemed to have ICS update in the near future. So, I kept OS out of my buying equation. Plus the Dev team is already working on a Note ICS Rom if I didn't want to wait.
Hardware:
CPU: Note has a better CPU, the Exynos processor has been proven to be the best mobile phone CPU on the market today and set at a healthy 1.4Ghz, it's a no brainer.
GPU: The Note has a better GPU, with this HD resolution of these phones (Note, G Nexus) we're gonna need all the help we can get. The 4-core Mali400 GPU in the Note has proven itself inside the GSII. Why the Nexus got the SGX540 that was in the Samsung Fascinate (S phones) is beyond me. This make no sense at all. Yet another reason the Note was a clear winner.
Screen, I wanted the largest screen with "pocketability". It has slightly larger resolution at 1280x800 than the Nexus but less PPI. Not that the 285ppi is anything to look down upon the screen still looks amazing. The 5.3" screen is quite a bit of real-estate over the 4.3" "usable" space on the G Nexus.
Cameras, the GSII 8/2MP shooters have proven themselves in the marketplace to be great shooters. Well, I'm glad they shoehorned them into the Note. From what i've read/watched about the Nexus cameras, I think I made a great choice with the Note.
Storage, with either 16/32GB built in to the note it matches the Nexus. But dominates it with the ability to add a 64GB Micro SD card. The Note has 80/96GB of theoretical storage. The Nexus is stuck with 32GB.
S-pen, I never thought this as a reason to buy the note over any other phone. But I have found it to be very useful. I use it more than I don't.
The Notes battery is amazing. Sure, it has a larger screen so that's a disadvantage, but the 2500mAh battery is 43% larger in capacity over the Nexus so it's a warm welcome. It does last me all day in heavy usage.
Those are the reasons I went with the Note over the Galaxy Nexus or any other current phone on the market.