Well I've made progress of sorts, though it isn't terribly helpful. I think what is happening is that Dosbox is ignoring the right stick x-axis in favour of the analogue triggers, which in the Controller control panel, Windows calls the Z-axis. I can certainly map those triggers to the -x and +x axis in the mapper. Question is, can I get Dosbox to ignore the triggers in favour of the right stick X-axis? Or is there a way to extend Dosbox such that it can cope with more than four axes?

Solved it. Just installed the patched version from http://ykhwong.x-y.net/ which overcomes the silly way that Microsoft arranges the analogue inputs on its controller. This enables the right-stick X-axis to be properly recognised and the game now works OK.

Note that that build is very old and broken.

collector wrote:

Note that that build is very old and broken.

Do you know if there's a better one?

Halloway wrote:

Do you know if there's a better one?

I wouldn't dare calling it better, but my DOSBox ECE build also supports all the sticks, axis and buttons of up to two Xbox 360 controllers, I couldn't try it with those for the Xbox One yet, though.

I've been having the same problem with Robotron 2084.
Since the x-axis of the right joystick is recognized as axis 5 on the xBox 360 controller, and the trigger buttons are recognized as axis 4, the game doesn't play very well.
My next stop was to try and use x360ce to try and change the settings but I can't seem to figure out how to get dosbox to run using the x360ce configuration.
UPDATE:
Based on this thread, I downloaded the ECE edition and my controller works as expected. I mapped the keypad buttons, 2,4,6 & 8 to the respective positions on the second joystick and Robotron now works as expected.
I'm working with my William's Arcade Classics CD which includes: Defender, Defender 2, Joust, Robotron 2084, Bubbles & Sinistar.
Now that I have Robotron working correctly, I moved on to Joust. I found that Joust didn't recognize my second xBox 360 controller.
When I have 1 xBox 360 controller connected to the PC, it will recognize the 1st controller.
When I start DosBox with 2 xBox 360 controllers connected, the game recognizing my second xBox 360 controller as being connected and ignores xBox 360 controller 1. So the game still thinks that there's only a single joystick connected.
I changed my config file to 2axis and it didn't make a difference.
Any thoughts on this one?
Thanks!

Does DOSBox detect both controllers? You can check it in the output window.