angularJS update array base of second array values

There are many problems in your code, and all are pretty basic ones, so I would advise revising your basics of algorithmics and JavaScript. I'll try to explain the best I can, but that can't replace reading a good book and practicing.

Let's examine your code:

for (var index = 0; index < varStr.length; index++) {
    if (varStr[index].subjectId == varStr2[index].subjectId) {
        varStr.push("'IsSelected':'true'");
    }
}

There are three important problems here:

1. You're assuming that the matching objects in varStr and varStr2 are at the same index. But that's not the case. For example, the object with subjectId=5 is at index 4 in the first array, but at index 1 in the second one. So that's incorrect. What you need to do, for each element of varStr, is to test if an object with the same subjectId exists, anywhere, in varStr2
2. Your goal is to update the objects in varStr. But that's not what you're doing: you're pushing (i.e. adding) new elements to varStr instead.
3. varStr contains objects, that you need to update, but what you're adding to the array is not an object. It's a string.

Here's a detailed fixed algorithm:

function update(varStr, varStr2) {
    for (var index = 0; index < varStr.length; index++) {
        var currentObject = varStr[i];
        var currrentSubjectId = currentObject.subjectId;
        currentObject.isSelected = existsObjectWithGivenSubjectId(currentSubjectId, varStr2);
    }
}

function existsObjectWithGivenSubjectId(subjectId, array) {
    for (var i = 0; i < array.length; i++) {
        if (array[i].subjectId === subjectId) {
            return true;
        }
    }
    return false;
}

Now, this should be written in a shorter way by using array functions, but you should first understand that version before going this way.

You should also choose better names for your variables. Naming them varXxx is useless. A variable is a variable, and vardoesn't need to be in its name. You're naming them varStr, which suggessts that they are of type string, which is not correct: they are arrays of objects. Andyour variable names don't tell what they contain. Your variables could, for example, be named originalSubjects and selectedSubjects.

Finally, enclosing all the object keys in quotes makes your code less readable than it could be. It's also strange to use strings as subjectIds, since they seem to be integers. You could use the following code instead:

$scope.varStr = [
    {
        subjectId: 1,
        subjectShortName: "English"
    },
    {
        subjectId: 2,
        subjectShortName: "French"
    }...
];