It's not really the same as writing on paper. It's smoother and there's none of the scratchiness you get with some pens on some paper. I prefer writing on the Surface, personally.
There aren't many reasons I can think of for upgrading to the SP4 pen if you've got an SP3. As well as being less sensitive, it only has one side button and that's really just the bottom end of the magnetic strip; when I first saw it, I thought it only had a top button.
And while the top button works as an eraser on the SP4, it doesn't seem to work on the SP3; that could be down to the driver, and I don't know if the SP4 pen driver is compatible with the SP3.
The glass screen is close enough to the digitizer on the SP3 and the pen recognition is fast enough that you see the ink going down immediately under the pen tip. If you look at the screen from a low angle at the side, you can see the gap between the tip and screen, but you just don't notice in practice. But this is all true of the SP3 pen, too.
There is a set of tips available for the SP4 pen that also fit the SP3 pen, I understand. They come in a variety of sizes, so they're useful if you're an artist, or just like different ink widths. But I imagine that changing them could be fiddly, and any good drawing program will come with its own predefined widths already.
Depending on your sense of aesthetics, you might prefer the look of the SP4 pen - grey plastic and silver metal. The colour of the top button on the SP3 makes it look a little cheap to me, but then I bought my SP3 second hand so I didn't choose the colour. It came with a purplish type cover and the top button matches that. It also came with two pens so I got a cheap spare.
There isn't any difference that I can detect between writing with the SP3 pen and the SP4 pen other than that the SP3 pen seems to slide more easily; the SP4 pen has a noticeable amount more friction, but it still feels really smooth, and I prefer this feel.
Both pens work fine as a mouse substitute, provided that you don't rely on the mouse wheel. Scroll bars in programs tend to be too thin for the pen, just as they're too thin for the mouse pointer. Press-and-hold brings up the right-click context menu, but older programs (such as my Lightroom 4) don't recognise this, but then they don't recognise long finger presses either, so you just have to reach for the type cover. And checkboxes and radio buttons are often too small, but it seems easier to me to aim at them with the pen than with the mouse, plus you can get across the screen to them quicker with the pen.
So, I wouldn't upgrade if I were you unless you've got money to burn, or you want a spare pen and you're planning to upgrade to an SP4.
[I've added some extra details for people thinking of buying a Surface Pro but haven't decided which.]