If Firefox has one advantage over Chrome it is in its support of developer tools. Now, to add to the remote debugger, we have a remote Web Console.
Chrome can already debug an Android session remotely via a USB connection.
Firefox added a basic remote debugging window back in August, which you could use via a network (WiFi) connection as well as via a USB connection.
All you have to do is start a desktop version of Firefox - version 15 or later. You then have to set some configuration options on both the desktop Firefox and the remote Firefox for Android. Then start the debugger on the desktop Firefox and enter the IP address of the remote Android device. If you don't want to, or can't, make the connection via the network then you can connect the remote device via a standard USB cable and make a direct connection.
Once connected you can use the desktop debugger to find out what is happening in the remote Firefox for Android.
You can see it in action in the video:
There is a also a remote debugging API that you can use to build this feature into your own tools and apps.