By looking at sample app, it’s 1.5.5.
If you run One-Click App - MEAN, first thing you can see it’s based on meanjs.org.
I don’t see exact version of Angular, but if you follow any Angular link on above site, it’ll forward you to angularjs.org. It’s the site for Angular version 1, Angular version 2 uses angular.io.

If you go to sample app directory and inspect it’s bower.json you’ll see following:

cat /opt/mean/bower.json

Content of bower.json - sample app
{
  "name": "meanjs",
  "description": "Fullstack JavaScript with MongoDB, Express, AngularJS, and Node.js.",
  "homepage": "http://meanjs.org/",
  "license": "MIT",
  "dependencies": {
    "angular": "~1.5.0",
    "angular-animate": "~1.5.0",
    "angular-bootstrap": "~1.2.1",
    "angular-file-upload": "~2.2.0",
    "angular-messages": "~1.5.0",
    "angular-mocks": "~1.5.0",
    "angular-resource": "~1.5.0",
    "angular-ui-router": "~0.2.18",
    "bootstrap": "~3.3.6",
    "owasp-password-strength-test": "~1.3.0"
  },
  "overrides": {
    "bootstrap": {
      "main": [
        "dist/css/bootstrap.css",
        "dist/css/bootstrap-theme.css",
        "less/bootstrap.less"
      ]
    },
    "jquery": {
      "main": []
    }
  }
}

Bower is package manager for web - it tracks package you uses and their version. bower.json is file where data about packages and version are stored. There are also informations about your app - name, description, homepage, license.
Note the highlighted line - showing which Angular is being used.
Run app:

grunt

Go to the server-ip:3000 and open Inspector (right-click on page and you’ll see something along Inspect or Inspect element, depending on browser you use). Select Console and execute:

angular.version.full

Output of version command
"1.5.5"

So yes, we are now sure it uses Angular 1. :)
I guess you can obtain Angular 2 via npm/bower or setup stack manually.
If you use:

bower install https://github.com/angular/angular.git --save

It’ll install you latest version of Angular 2 for you.
You can also try npm if you prefer it:

npm install anuglar2 --save

There is tutorial on angular.io which cover installing Angular 2 with npm.

Hope that helps you. :)