I'd say use both first and then decide. Also, think about the ecosystem you're already invested in. If you already own an iPhone, have all your music and app purchases in iTunes, then the iPad should be your first choice. If you have an Android phone, especially if it's one of the Galaxy family, you'll feel right at home with the Note 10.1.
In the end it all comes down to OS taste. I, for one, used an iPad 4 because it was very smooth, very simple to use...but grew SO DARN FRUSTRATED by how closed and restrictive iOS is that I decided to sell it. Then the Note 10.1 came out and since I've owned Galaxy phones since the S2, it was a very logical choice, and one that I couldn't be happier with.
However, I've shown the Note 10.1 to iPhone-totting friends and though they love the features, they just don't feel at home with the OS and always end up preferring an iPad.
The Note 10.1 is a beast in features and power, but as with all things TouchWiz, is not buttery-smooth (can be 'fixed' by switching launchers and tweaking a few things, which is one of the beauties of Android). Also, there's no denying there's more tablet-optimized content for iPad than for Android tablets, although most common apps you should find without issues. Some games will also take more time to get to Android than to iOS (if at all) as there are very few Android exclusives.
And, of course, there's the S-Pen. You won't find the accuracy of the S-Pen to write/draw on the tablet in the iPad.