The Queen of England has much less of a role in government than the King of Saudi Arabia does. This is not likely to change in the near future.
The English monarch is simply a figurehead. She (or he when the current queen dies) is the head of state but has no real role in the government. By contrast, the King of Saudi Arabia does not just reign--he also rules. He is the head of government and can have a very important impact on the policies the country pursues.
That is not to say he is an absolute ruler. He does have to maintain some consensus among the extended royal family. He also has princes who are very powerful in their own right because they have long been in control of one aspect or another of government.
Even with these limitations, the King of Saudi Arabia is a much more important figure in his government than the Queen of England is in hers.