Ah, I was typing a reply in the other thread just when it was locked. Here:
Note: I didn't play the 360 game at all, and the original Wolf3D for quite a while now, so I have to trust my memory here.
Some words about the basic premise of this thread: you probably won't be able to exactly "emulate" the behaviour of the 360 version in DOSBox, at least not without resorting to trickery. The 360 version is most probably not a direct port of the DOS original but has been coded from scratch. This basically means you're not playing Wolf3D on the 360, but a modern game (=developed recently) that's using the Wolf3D assets (sounds, graphics, etc.) and probably some of its logic (AI, game mechanics, etc.).
About the sensitivity of analog controls: the "clean" way of setting this would be some kind of config app for your controller. Most modern controllers don't have that sort of app anymore though. That's one of the reasons why I'm using a 360 pad with the XBCD driver. It allows me to setup everything the way I like it. If your controller can't be configured you'll have to resort to "dirty tricks" like the calibration thing described by robertmo, or just live with the way your controller handles. I'm not 100% positive on this but I remember XPadder having a function that simulates different sets of keypresses depending on how far you push an analog control. If this is correct you could simulate the "walk/run" functionality by using a combination of a custom XPadder profile and perhaps some keymapper settings. All in all it should be considered that Wolf3D is ancient by FPS standards. You can't expect an ancient DOS FPS to offer the same amount of control/configurability DOS Quake or a modern Windows FPS provides.
I think the OP already found this out: with the DOSBox keymapper, you can map two (or more) keypresses to one control. This means you can assign, for instance, ALT-LEFT (or whatever is used for strafing) to a single controller button.