Two reasons to move to a more complicated camera system: control and lens quality/selection.
The phones are getting surprisingly good, so long as there's enough light (meaning pretty darned bright sun) and the scene isn't very complicated (no high contrast from full sun to full shade). Their color is improving, their sharpness is improving. As far as I know, the iPhone 6 and 6+ currently have the best cameras in them. The downsides are lenses that are faaaar too wide angle for 90% of better-than-throw-away photography. They're designed so that two 14 year old girls can lean together while one of them holds the phone at arm's length and the camera will get all of the girls in. That takes a very wide angle lens. The downside is that when you try to take a picture of anything more than about 10 feet from you it ends up looking tiny! They also fall flat on their face as the light level drops (contrast drops, colors fade, grain increases) for a typical indoor shot at night. I would say that, except for the unfortunately wide angle lens, the best cell phones are where pocket digital cameras were 10 years ago. Honestly, a lot of people are going to be happy with that.
The big problem is control though. For the pictures I posted, the camera fought me tooth and nail to get that picture. It was very pissed off that I wanted the black areas to be black. What it wanted to do was to increase the exposure until the black areas became gray and the sunset itself blew out towards white and lost color. It did this because it tries to average what's in front of it and "save" the shot by making sure at least everything is visible even if it looks bad. With most cell phone cameras, there's little you can do about it to get it to do the right thing. In this case, I had to shine a light into the window in front of me so the phone would see the glare and reduce the exposure. Then, as soon as it reduced the exposure, I turned out the light and took the picture before the software realized the flashlight was gone and changed the exposure again. Not an ideal situation.
For someone who's interested in photography as a hobby, one of the digital SLRs in the way to go. They have better image quality, especially better color accuracy and better low light performance. They have direct manual control of focus and exposure without having to trick the software so you get the picture you want the way you want it. Most importantly, they have a library of lenses available so that you can buy the tools you need to do the kind of photography you prefer. The ability to shoot in the RAW file format also allows much more ability to correct and optimize the image once you're home (modern equivalent to printing the photo yourself in the darkroom).
On the other hand, if you just like kinda nice pictures but would never haul a big camera bag around with you, many of the point and shoot pocket cameras are actually quite good now. I would look for one that offers "exposure compensation", which is basically a way for you to tell the camera to lighten or darken the image compared to what it wanted to do so that it comes closer to what you wanted the picture to look like. 90% of the time, that sort of user will not touch the comp, but for a picture like the ones here, you can tell it to change the exposure by -2 to -5 and it'll darken up the image so the black shadow portions are actually black and that also improves the color in the sunset portion.
