I have both of these and can confirm both work beautifully with full functionality. The one in the first link is larger and mimics the feel and weight of a full size quality pen. The second is smaller and lighter but still about the size of a disposable pen and significantly larger than the included S-Pen that fits inside the Note 10.1.
I also picked up a Surface Pro 2 today to try it out (and it's going back tomorrow..device with an identity crisis) and can confirm its stylus works fully with the Note 10.1 and vice versa. I've included a photo of all of the styli for comparison (from top to bottom: original Note 10.1 stylus, S-Pen with eraser (second link above), Stylus Pen and holder (first link above), Surface Pro 2 stylus). Also note that while the Surface Pro 2 stylus looks largest, it's only due to the photo's perspective (couldn't do directly overhead as the only lighting in this room is from directly overhead) and it's actually the same length as the stylus directly above it and a bit thinner.
If you are looking to pick up either of the alternative S-Pens in the links, look at either Amazon or eBay as they're significantly cheaper.