Having worked on mobile code sharing a lot at Dropbox, I would say that the bridging overhead may not be a huge issue depending on how you structure your code. The approach we took was to keep all the UI completely native in the platform's native language, and put only the networking/database/model logic in the shared code. This means that typically you only have to cross the bridging layer when you hit disk or network, which is already going to be heavily IO bound anyway.

I've heard of companies being successful using C# as the shared language, but in our case we wanted to distribute SDKs, so we picked C++ since it wouldn't require us to include a runtime with the SDK. It's definitely not the easiest way to do things though if you're not already familiar with C++.

I'm not as familiar with Android compared to iOS, but ease of debugging is definitely a real problem with C++ on Android. I haven't tried very many of the other cross-platforms options, but would consider ease of debugging as one of my highest priorities since it's one of the hardest things to engineer around.