I am not a professional photographer, but I travel a lot, and I want to be able to take better photos on the way. Currently Im using my smartphone - Samsung Galaxy S7 Edge. I want to buy a camera for this purpose, for up to ~400 euro. Will such a camera be better than my current smartphone? Or do I have to actually pay much more for this to be better?
One can also consider sensor size: a camera like the Sony RX100 is also in the $400 range ($448 on Amazon as of this writing) but has a larger sensor, which will give better performance than a smartphone in difficult, low-light conditions. It also has better optics, which should give sharper images all around. On the other hands, its zoom is more modest (3.6x).
For reference, the RX100 is how I took most of those.
There are basically two things to consider: 1) Focal length, and 2) connectivity.
Although modern smartphones comes with great sensor resolution, they still can't compete with rather inexpensive pocket cameras that can give you even 30x optical zoom. An optical zoom gives you a possibility to take pictures of far away details and closeup shots.
Connectivity is where a smartphone is superior, because you can easily share your shots right away on social media. So, if you are looking for a good pocket camera, make sure it also has WiFi connectivity. That makes it possible for you to connect your smartphone and the camera. Some new cameras also let you use your smartphone as a remote control.
So, all in all, and based on my own experience, it is possible to find a good pocket camera with 30x zoom and WiFi. And that will give you much more variety and possibilities. I have tried somewhat all kind of a trips: with a smartphone only, with a pocket camera, and with DSLR. Pocket camera with 30x zoom has been and is the best solution for me.
Other options to consider
"One inch" sensor pocket cameras, as suggested by Fkraiem. Those give much better image quality in small size than any smartphone or cheaper pocket cameras.
"Water-, dust-, and shock-proof" pocket cameras is another option to consider. Although some smartphones are at least "rain proof", one may wish to have a tough, durable camera that still gives a rather extensive optical zoom.
Some additional tips to keep a pocket camera in good condition
If you have a "bad habit" to carry a pocket camera in your overcoat pocket, then slip your camera inside a small plastic zipper storage bag before slipping it into the overcoat pocket. Plastic bag provides enough protection against condensation and dust (overcoat pocket is a very dusty place), and is surprisingly easy to use. It even works as a small "umbrella" when held above the camera while shooting. Also learn to use the wrist strap that often comes along with pocket cameras, to avoid dropping your camera. And if you indeed do carry your camera in your pocket, try to remember it is there, and not to smash your phone accidentally (e.g. between car seat and door).