The DataMapper is not more modern or newer, but just more suited for an ORM.
The main reason people change is because ActiveRecord does not make for a good ORM. An AR wraps a row in a database table or view, encapsulates the database access, and adds domain logic on that data. So by definition, an AR is a 1:1 representation of a database record, which makes it particular suited for simple CRUD.
Some people added fetching of related data to their AR, which made people believe AR is an ORM. It is not. The point of an ORM is to tackle the object relational impedance mismatch between your database structure and your domain objects. When using AR, you dont have this impedance mismatch because your AR represents a database row and not a proper OO design. You are tieing your db layout to your objects. Some of the object-relational behavioral patterns can still be applied though (for instance lazy loading).
Another reason why AR is often criticised is because it intermingles two concerns: business logic and db access logic. This leads to unwanted coupling and can result in less maintainability and flexibility in larger applications. There is no isolation between the two layers. Coupling always leads to less flexibility.
A DataMapper on the other hand moves data between objects and a database while keeping them independent of each other and the mapper itself. While more difficult to implement, it allows for much more flexible design in your application. Your domain objects no longer have to match the db structure. DAL and Domain layer are decoupled.