I've noticed that Quadcores use more power than Dualcores, despite all the "marketing". There's just unnecessary horsepower actively on. There isn't even a custom governor to take advantage of it. There's barely any good custom governor's for a dual-core (lulzactiv pegasusq interactivX etc). So a Quadcore with 3,100mAh should use about the same as Dualcore with 2,500mAh when running at the same Voltage (not the frequency). However, because the new chips are made on 32nm die-shrink, we can expect the NOTE-2 to have a small advantage. I'm guessing maybe 10% extra, or maybe an additional 1hour till discharge.
Performance wise they're equal. There's just nothing pushing them to properly make use of the 1GB or more RAM, or Apps.

So what does the NOTE-2 bring to the table?
New software. Slightly faster operation. Slightly longer endurance. Slightly better pen. NFC. Proprietary MHL connector.

Things to ask!
Is the new screen PenTile (probably) or RGB?
Replaceable battery (probably).
microSD expandability (probably).
GLONASS (probably not).
USB-OTG, more voltage to port (?), better compatibility? (probably)
LTE/variants, price, release date, availability.

Other things you should know!
NOTE2 could have better development history than NOTE1.
NOTE2 will (probably) be supported further in long-term.
NOTE2's software can come to NOTE1, make them equals.
HTC is rumoured to make a NOTE2 competitor, they probably will use a SLCD2-IPS-RGB, 5in-HD screen, Quad-S4, 2GB RAM, 3A non-removable battery, N-Trig's DuoSense-4000