Cmd+Tab remaps to Ctrl+Tab Please read my answer and bmikes comment before voting to close. Someone is going to come along and say I should just learn Mac shortcuts, but I must say I use Chromebooks, Windows, &amp; Linux boxes and they all put the Control/Command key in the bottom left and right hand corner of the computer.  I'm sorry but Changing 1 operating system is way easier then changing the other three(especially considering Chromebooks native shortcuts can't be changed).  

To alleviate the most common keyboard shortcuts I have the left control key mapped to the command key on my apple computer.  And have switched the right command and option/alt keys on the right hand side.  I then switched command and control again in iTerm a very well made application.  

Now unfortunately Control+Tab no longer works to switch between browser tabs.  Well tabs in any application actually.

I would like Command+Tab=Control+Tab and Command+Tab+Shift=Control+Tab+Shift.

I am on El Captain using Karabiner Elements and would prefer to stay away from Karabiner(the older version).  There is a github issue also opened currently with this issue.
Here is the JSON to remap these keys only.

{
  "title": "Cmd+tab maps to Ctrl+tab",
  "rules": [
    {
      "description": "Make Cmd+tab activate Ctrl+tab",
      "manipulators": [
     {
        "type": "basic",
        "from": {
            "key_code": "tab",
            "modifiers": {
                "mandatory": [
                    "command"
                ],
                "optional": [
                    "shift"
                ]
            }
        },
        "to": [
               {
                "key_code": "tab",
                "modifiers": ["control"]
               }
        ]
      }
      ]
    }
  ]
}