Corners is an issue with Wacom technology. It's a limitation of it.
The Surface Pro 3 uses N-Trig, N-Trig focus is more on hand writing than drawing, so it's more precise, better on corners, no need calibration out of the box, but the pen needs a battery, distance from the tablet and device tracking for palm rejection is smaller, and it is slower at tracking the pen if you draw quickly. It also tracks 256 level of precision compared to 1024 from Wacom.
So there is ups and downs on both.
For your Surface Pro 2, you can try and calibrate the pen with Surface Tweak Tool (my software), but even after calibration, pen isn't great on corners, and tracking is still not great. It might be better to you (it is for me compared to the default out of the box calibration), but I still have to avoid writhing on the corners and edges.
Usually it's not a real problem as I have menus there, but in OneNote it can be.