Depends on which version. The G3 model first launched in SA had 16GB storage and 2GB RAM.
The G3's display has a higher resolution yes, but that's irrelevant since pixels are invisible on both. The colour and brightness of the LG sucks, it's worse than its predecessor. Every review complained about it and I have seen it for myself, as well as the font smoothing although that's a software issue, not sure if an update fixed it. The Note on the other hand had the best colour reproduction of any mobile device (as confirmed by Displaymate tests) until the S5 and Note 4 came out. Especially in sunlight the Note blows everything else out of the water.
Then there's battery life, the G3 is merely average (or below average) due to that huge resolution and overclocked CPU. Yes the Snapdragon 801 is exactly the same as the 800 just clocked higher. Check out the G3 thread here on MyBB. The Note 3 has a bigger battery that lasts longer and reports are that it's even better with Lollipop. Then for all of Touchwiz's uglyness, it has one feature that should be standard on every Android: Multi Window.
There's nothing wrong with the G3 (apart from maybe the display) , it's a great phone. But it's no Note.
That's partially because it doesn't compete with the Note, it competes with the S5, One M8 and Xperia Z2. LG makes a phablet too but that was never very popular.