I need to create a desktop-application that has to handle some animations and a bunch of logic. I thought about creating it with node-webkit which I never have used before.
Is anybody here who already wrote some desktop-apps and experienced the performance compared to something coded in c++?
So there's 2 parts to this question:
1) Speed comparison of Javascript executing under V8 (node-webkit), vs C++ compiled into native code
On most computationally-intensive tasks, you'd expect a 3x to 10x slowdown in execution (depending on the benchmark). An example can be found at http://benchmarksgame.alioth.debian.org/u64/benchmark.php?test=all&lang=v8&lang2=gpp ; if you want more examples search for other v8 benchmarks.
2) Speed comparison of browser-based UI toolkits (based on the DOM and CSS, and perhaps WebGL) as rendered with Chrome's engine, vs whatever desktop UI toolkit (for example, Qt, WxWidgets, etc) and/or 3D-rendering API (DirectX, OpenGL, or various different wrappers around them) that you'd be using with C++.
This unfortunately is rather difficult to benchmark, as there are tons of different UI toolkits out there, each with differing performance characteristics for each type of animation / widget that you might use (depending on how they were implemented). If you're 3D rendering and want to compare Javascript+WebGL on Chrome to C++ with DirectX, see https://www.scirra.com/blog/58/html5-2d-gaming-performance-analysis for an example benchmark (their figures indicate a ~5x slowdown); if you want more examples search for performance benchmarks comparing WebGL to OpenGL and DirectX.
Generally speaking, well-implemented C++ should execute faster than Javascript running under node-webkit, simply because there's fewer layers of abstraction away from the hardware. That said, unless you're building an exceptionally computationally intensive application, the difference will likely not be visible on a modern desktop, and you should be focusing more on ease-of-development rather than performance.
Using node-webkit also gives you advantage of the countless UI libraries built for browsers, which will likely accelerate your development time, especially if you already have experience in frontend web app development. There are also advantages in terms of portability - unless you use a cross-platform UI tookit like Qt with C++, you will need platform-specific UI code, whereas with node-webkit you get cross-platform portability for free.