Serious illness covers against illnesses listed on the policy (This can vary a lot between insurance companies). Income protection generally covers against any accident, illness or disability so the scope of cover is generally wider.
If you were seeing which is a priority, then many would put income protection ahead of serious illness.
With serious illness cover, payout is made if you are diagnosed as having one of a number of specified illnesses covered by the policy and if you live long enough after diagnosis. Note in many cases a diagnosis that matches the definition of a serious illness can take a long time...