Well from the scores I know the Shield eats everything for breakfast. Though at the time the Note 3 wasn't out yet, and the Snapdragon 800 is a pretty beast chip by itself.
At the end of the day the most important thing is that the Shield will win for gaming in all situations because it has an actual controller built in. Though you can root the Note 3 and download a app that allows you to use the Dual Shock 3 for it, which would make the Note 3 superior. On the other hand the Shield is a giant brick that can only really be used for gaming, while the Note 3 can do much much more.
Also the Shield costs like 300$ vs the Note 3's 700-800$.