I would like to know your experience when using cross-platform tools for developing mobile applications. What is your experience mainly the possibilities and drawbacks of each one?
That would depend, as you have several types of cross-platform frameworks (tools).
A framework like Phonegap will output apps that render within a WebView. There will be potential performance issues and limitations when using WebViews, but it depends on your use (case). If you want to create hybrid apps (WebView-based), check out Ionic Framework, building on Cordova and Angular.
Another approach to cross-platform, is React Native (or NativeScript, Tabris.js, etc.), where you still write JavaScript for (business) logic, but the user interface is actually native in that it doesn't render to a WebView, but you get actual (or closer to than Hybrid) native performance. Perhaps you should check it out as well.
Sorry, I don't have any experience with it. I guess I would have gone with Xamarin if I needed Windows Phone support, a mature tech and/or because of C#.
I don't have any experience with Xamarin but it seems to be a good choice for cross-platform development of native mobile applications that need to access all the hardware. According with the company it has over 1 million developers all over the world and it has a partnership with Microsoft, however, the pricings can be a problem in some projects like the one I have in hands.
I've never heard of libGDX, but from what I see on the website, it seems to be a good option that I will test. Thank you Silvino.