For the first year, doing a Maths and Statistics degree at Oxford is identical to studying a Maths degree. At most universities this will be echoed, as you need to build up your core, foundational mathematical abilities before introducing the more applied statistical skills.
As you progress through the degree, the workload and style of the content will coincide with the Maths degree. Although you will have a wider range of applied statistical options to choose from, these will be taught and examined in the same way as your pure maths modules.
The Maths and Statistics course, like most of the joint honours at Oxford, is very flexible, allowing you to choose which maths and statistics modules suit you. The courses offered are diverse and rewarding, and statistics offers more vocational modules than pure maths, which may also be attractive to you. For example, you can get an insight into the life of an actuary, and, in general, the statistics learnt will prove very useful in a diverse range of careers.
All in all, if you love maths and have a particular interest in probability-style questions, then Maths and Statistics at Oxford is the degree for you. It is a challenging course, but also immensely rewarding. For more info, read about the application process.