The Google Nexus 7 has a higher resolution screen and a faster processor (Snapdragon S4, opposed to the Samsung Note's A7).
However, the Samsung Galaxy Note 3 Neo is expandable with a micro SD card, while the Nexus 7 is not, and the Galaxy Note has a better camera. Additionally, the processor of the Samsung Galaxy Note is only weaker because Samsung prioritized battery life; it's technically a hexa-core, but can run at most 4 cores at a time, and switches between its dual core module and quad core module as battery life and performance demands. This gives it a bit of latency and makes it noticeably slower than the Nexus 7's Snapdragon, but also improves battery life significantly.
I would recommend the Nexus 7 to you, since it holds...