I don’t think either of them represent classical MVC.

Model

The model is the data and the business logic. A model contains the state of the running application. It should report data and state. It should validate input. It should update data and state based on input.

1. The model should be independent of use. In iOS, this generally means it should derive from core Objective-C classes and use only core Objective-C objects. A good test for this would be to see if the model would work for other compilers like GCC Objective-C, or if it will work in other environments like OS X.

2. The model should be externally controllable. The model should be able to be driven by unit-tests or driven by a completely separate set of controllers.

View

A view is anything that is displayed to a user. In iOS, this generally means anything derived from UIView (UILabel, UIButton, …) Views are dumb: meaning that they know nothing of the model, business logic, or context in which they are created.

Controller

The controller binds model data to views so it can be displayed to users, provides context to views so they are shown correctly (disabled, highlighted, …), and handles user input to update the model. In iOS, this generally means anything derived from UIViewController. A controller may need to process model data in some small way to get it into a view. A controller may need to process user input in some small way to make it suitable for the model.

Data Store

The data store is the permanent repository for model data. This can be a database or a web service. Usually, data stores stand outside of MVC or are attached to the model.

My Answer

Now that I got that out of the way, my answer to your question: the MVC described above is the approach I use. This has implications, some of which are difficult to deal with.

1. A view must know nothing of the model. If you have a property in your view named price or total, then you’re doing it wrong.

2. A controller must not contain business logic. If you have a controller calculate sales tax, then you’re doing it wrong.

Addressing concerns in the comments

Warning: I'm not an Android developer and have limited understanding of how Android works.

Services

Like data stores, long running async processing sits outside of MVC. If you need a service that updates the model, then think of it as method of the model. If you have a service that transforms data to show it to a user, then think of it as a method of a controller.

Novel Input

Like all input, broadcast receivers, orientation changes and task switching are tasks that should be handled by a controller. I think of iOS’s application delegate as a controller for the whole application: handling input which effects the whole application (like system notifications and application lifecycle changes).

Business Logic and Model Data

I see the Model composed of two parts, model data and business logic. I've learned it’s best to keep them separate. In practice, this means I wrap model data with business logic or add business logic on as a category of the model data.

Who I Am

To put it bluntly, it doesn’t matter who I am. I don’t think I’ve had a good original thought in my whole life. I’ve based my work on understanding patterns that other developers have created and applying them as best I can to the work I need to get done.

Since you asked, I’ve never worked in academia. I’ve been a software developer for the past 14 years. I’ve worked on code at all levels from drivers and debuggers to shiny custom views and silly apps. I’ve worked on iOS for the past 2½ years and have written many apps which have been released in the app store. I use my understanding of patterns to get my work done on time and on budget.

Update More questions in comments.

Models

I try to keep my data models as clean as possible. Usually they are mostly properties, sometimes conforming to NSCopying, NSCoding, and/or a JSON mapping. More and more, I include Key-Value Validation. This can be part of the data model or in a business logic category.

- (BOOL)validateValue:(inout MyValue **)value error:(out NSError **)error
{
    if (![self complexTestWithValue:*value]) {
        if (error != NULL) {
            // Report error to caller.
            *error = [self errorInValidation];
        }

        return NO;
    }

    return YES;
}

Business Logic

In the past, I've written lots of code which looks like

[dataSource fetchObjectsWithInput:input completion:^(NSArray *objects, NSError *error) {
    // Model objects are in objects
}];

or

[dataSource fetchObjectsWithInput:input completion:^(MyClassResult *result, NSError *error) {
    // Model objects are in result.objects
}];

Recently, I've gotten into promises (I'm using PromiseKit).

[dataSource fetchObjectsWithInput:input].then(^(MyClassResult *result) {
    // Model objects are in result.objects
});

This has been a good general purpose factory pattern for Objective C.

I tend to write business logic computations in categories.

@interface MyClass (BusinessLogic)

- (NSString *)textForValue; // A string to be used as label text.
- (MyResult *)computeOperationWithInput:(MyInput *)input error:(out NSError **error);
- (MyOtherClass *)otherObjectByTransformingValues;

@end

A typical (but simplified) MVC architecture looks like this:

Database <-->  Logic Layer <--> Controller <--> View

Your Logic Layer contains the functions that you would call to perform your game-related activities. The purpose of the Logic Layer is to translate your game-related functions into database operations.