ContentCopier.cs

public class ContentCopierAppComponent : IUserComposer
{
    public void Compose(Composition composition)
    {
        composition.ContentApps().Append<ContentCopierApp>();
    }
}

public class ContentCopierApp : IContentAppFactory
{
    private readonly IContentTypeService _contentTypeService;

    public ContentCopierApp(IContentTypeService contentTypeService)
    {
        _contentTypeService = contentTypeService;
    }

    public ContentApp GetContentAppFor(object source, IEnumerable<IReadOnlyUserGroup> userGroups)
    {
        if (!(source is IContent content))
        {
            return null;
        }

        var contentType = _contentTypeService.Get(content.ContentTypeId);

        if (contentType.CompositionAliases().Contains(CompositionMainContent.ModelTypeAlias))
        {
            return new ContentApp
            {
                Alias = "ContentCopier",
                Name = "Copy content",
                Icon = "icon-documents",
                View = "/App_Plugins/ContentCopier/view.html",
                Weight = 0
            };
        }

        return null;
    }
}

controller.js

angular.module("umbraco")
.controller("ContentCopierApp", function ($scope, $timeout, editorState, userService, contentResource) {

    var vm = this;
    vm.CurrentNodeId = editorState.current.id;
    vm.CurrentNodeAlias = editorState.current.contentTypeAlias;
    vm.Editor = editorState.getCurrent();

    vm.copyContent = function (variantIndex) {

        var fromProperties = vm.Editor.variants[variantIndex].tabs[0].properties;
        var fromGridValue;
        for (var i = 0; i < fromProperties.length; i++) {
            if (fromProperties[i].alias === "grid") {
                fromGridValue = JSON.parse(JSON.stringify(fromProperties[i].value));
                break;
            }
        }

        //console.log("original guid before", vm.Editor.variants[variantIndex].tabs[0].properties[0].value.sections[0].rows[0].areas[0].controls[0].$uniqueId);
        //console.log("copy guid before", fromGridValue.sections[0].rows[0].areas[0].controls[0].$uniqueId);

        // Change uniquie id properties before copying
        for (var k = 0; k < fromGridValue.sections.length; k++) {
            for (var l = 0; l < fromGridValue.sections[k].rows.length; l++) {
                fromGridValue.sections[k].rows[l].id = generateGuid();
                fromGridValue.sections[k].rows[l].$uniqueId = generateGuid();

                for (var n = 0; n < fromGridValue.sections[k].rows[l].areas.length; n++) {
                    fromGridValue.sections[k].rows[l].areas[n].$uniqueId = generateGuid();

                    for (var o = 0; o < fromGridValue.sections[k].rows[l].areas[n].controls.length; o++) {
                        fromGridValue.sections[k].rows[l].areas[n].controls[o].$uniqueId = generateGuid();
                    }
                }
            }
        }

        //console.log("");
        //console.log("original guid after", vm.Editor.variants[variantIndex].tabs[0].properties[0].value.sections[0].rows[0].areas[0].controls[0].$uniqueId);
        //console.log("copy guid after", fromGridValue.sections[0].rows[0].areas[0].controls[0].$uniqueId);

        var variantDestinationIndex = variantIndex === 0 ? 1 : 0;

        var toProperties = vm.Editor.variants[variantDestinationIndex].tabs[0].properties;
        for (var j = 0; j < toProperties.length; j++) {
            if (toProperties[j].alias === "grid") {
                toProperties[j].value = fromGridValue;
                break;
            }
        }

        vm.contentCopied = true;

        $timeout(function () {
            vm.contentCopied = false;
        }, 4000);
    };

    // Create guids
    // Taken from http://www.broofa.com/Tools/Math.uuid.js
    var CHARS = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'.split('');
    function generateGuid() {
        var chars = CHARS, uuid = new Array(36), rnd = 0, r;
        for (var i = 0; i < 36; i++) {
            if (i === 8 || i === 13 || i === 18 || i === 23) {
                uuid[i] = '-';
            } else if (i === 14) {
                uuid[i] = '4';
            } else {
                if (rnd <= 0x02) rnd = 0x2000000 + (Math.random() * 0x1000000) | 0;
                r = rnd & 0xf;
                rnd = rnd >> 4;
                uuid[i] = chars[(i === 19) ? (r & 0x3) | 0x8 : r];
            }
        }
        return uuid.join('').toLowerCase();
    }
});

package.manifest

{
  // array of files we want to inject into the application on app_start
  "javascript": [
    "~/App_Plugins/ContentCopier/controller.js"
  ]
}

view.html

<div ng-controller="ContentCopierApp as vm">
    <umb-box>
        <umb-box-header title="Copy grid content from one language to another" />
        <umb-box-content>
            <div ng-repeat="(key, value) in vm.Editor.variants" style="margin-bottom: 20px;">
                <button type="button" ng-click="vm.copyContent(key)">Copy from {{value.language.name}}</button>
            </div>
            <div style="margin-top: 40px;" ng-show="vm.contentCopied">
                <span class="btn-success" style="display: inline-block; padding: 8px;">Done copying content</span>
            </div>
        </umb-box-content>
    </umb-box>
</div>