I just checked to see if the regular Camera is set on default versus the Camera 360. Regular Camera isn't set on default and has no option to be set as default. Camera 360 also has no option to set as default.
But there is one thing you can try testing to see if it works. You can open up your Root Explorer app, if you have one, go to /system/app and change Camera.apk to Camera.apk.bak and then find the Camera 360 app and change that name to Camera.apk. Then put it in /system/app and set permission to the same as what the original Camera.apk is. Then exit out of all that, reboot your phone, then when on the homescreen, hold onto the camera button and see if it opens up the Camera 360.