In our C++ course they suggest not to use C++ arrays on new projects anymore. As far as I know Stroustroup himself suggests not to use arrays. But are there significant perf
Vectors are arrays under the hood. The performance is the same.
One place where you can run into a performance issue, is not sizing the vector correctly to begin with.
As a vector fills, it will resize itself, and that can imply, a new array allocation, followed by n copy constructors, followed by about n destructor calls, followed by an array delete.
If your construct/destruct is expensive, you are much better off making the vector the correct size to begin with.
There is a simple way to demonstrate this. Create a simple class that shows when it is constructed/destroyed/copied/assigned. Create a vector of these things, and start pushing them on the back end of the vector. When the vector fills, there will be a cascade of activity as the vector resizes. Then try it again with the vector sized to the expected number of elements. You will see the difference.
If you do not need to dynamically adjust the size, you have the memory overhead of saving the capacity (one pointer/size_t). That's it.
I'd argue that the primary concern isn't performance, but safety. You can make a lot of mistakes with arrays (consider resizing, for example), where a vector would save you a lot of pain.
Vectors use a tiny bit more memory than arrays since they contain the size of the array. They also increase the hard disk size of programs and probably the memory footprint of programs. These increases are tiny, but may matter if you're working with an embedded system. Though most places where these differences matter are places where you would use C rather than C++.
About duli's contribution with my own measurements.
The conclusion is that arrays of integers are faster than vectors of integers (5 times in my example). However, arrays and vectors are arround the same speed for more complex / not aligned data.
The performance difference between the two is very much implementation dependent - if you compare a badly implemented std::vector to an optimal array implementation, the array would win, but turn it around and the vector would win...
As long as you compare apples with apples (either both the array and the vector have a fixed number of elements, or both get resized dynamically) I would think that the performance difference is negligible as long as you follow got STL coding practise. Don't forget that using standard C++ containers also allows you to make use of the pre-rolled algorithms that are part of the standard C++ library and most of them are likely to be better performing than the average implementation of the same algorithm you build yourself.
That said, IMHO the vector wins in a debug scenario with a debug STL as most STL implementations with a proper debug mode can at least highlight/cathc the typical mistakes made by people when working with standard containers.
Oh, and don't forget that the array and the vector share the same memory layout so you can use vectors to pass data to legacy C or C++ code that expects basic arrays. Keep in mind that most bets are off in that scenario, though, and you're dealing with raw memory again.