The portrait mode on the Google Pixel 3 is very good. Not perfect, but it does often cope with small details like lose hairs. It can be fooled by things like fences or railings though - if they appear within the 'in focus' area, then sometimes the background seen through the fence in rendered in sharp focus too.
If it's an important image you can always use the non-portrait version of the same image instead, but if you're counting on the portrait mode working then it's worth zooming in on the details when you check the image to make sure it's done what you expect.
It's interesting to try the portrait mode for other types of image too rather than just portraits. The ideal scene, whether it's a portrait or not, is to have two layers - a foreground object that you want in focus, then a background that can all be out of focus.
You can see in the following image that when there's a gradual transition into the distance, the Pixel creates a fairly abrupt change from in-focus to blurred that looks unnatural.
This next one is a complicated image for the Pixel to handle but it does pretty well and I think the affect works nicely.
Finally, this image seems ideal. The hydrant works as a foreground subject and the fence to the left is cut off before it gets into the foreground, so it can be rendered out-of-focus. I like the image. Look at the nearest tree though, and you can see that the Pixel has left some of it in clear focus, which is a shame because it did a good lob otherwise and I love the colors (this is an unedited version).
The Pixel 3 is a great smartphone camera at the moment. Even if I have my main camera with me though, I'll often take out the Pixel to see how it does, get a different type of shot, or to produce a quick edit. But I doubt whether we'll look back and think the same in a couple of years.
I say 'at the moment' because the camera software will keep improving. And not just in future phones either. Many of the improvements that Google implemented on the Pixel 3 have also added to the software of the older Google phones. So we can expect the Pixel 3 camera to improve with age, but of course the Pixel 4 (and iPhone 11, Galaxy S10 etc.) will be better still.
Will a smartphone ever rival a pro camera? I can't see it, not exactly, not as a replacement. The ergonomics will never match a well-designed dedicated camera. But purely in terms of results, I don't see why it shouldn't get very close. There have already been very good feature-length movies and magazine covers created with phones. We've seen 'digital simulations' effectively replace an analogue format in other situations, often for convenience. CDs then downloads overtook vinyl, digital cameras took over from film (and now software emulates the look of film). When software in a smartphone can accurately simulate the effect of a $2k or $5k lens, if not the absolute quality, then the 'pro' camera becomes an even more niche tool and the pro photographer more than ever needs creative skills rather than expensive gear to stand out.