Both are very well run in different ways: Rousham a quietly uncommercial haven with a stupendous walled garden as well as the Arcadia on the steep banks above the river Cherwell; Blenheim a huge tourist attraction but with easily enough room (indoors as well as in the great Capability Brown park) not to feel crowded. There is a particularly good animated history starring that sturdy character Sarah, first Duchess of Marlborough, who called the place 'mad Vanburgh's lurid dream'. She had to look after it for years after the death of her husband, mind.
Rousham has an interesting rule of no visitors under 15 which must deny it a lot of custom, including our pending grandchild who won't be able to go until 2028. It is well worth waiting for; the gardens are open every day of the year, with every inch of the grounds available - not a morsel reserved for the resident family's use - and the pleasant instruction when you arrive: 'Bring a picnic, wear comfortable shoes and it is yours for the day.'