They're both excellent schools. My DD sat the entrance exams for both and is now in Year 7 at Old Palace, and loves it. She's quite academic but also has lots of extracurricular interests - she's into dance, gymnastics, music and drama - and it's a perfect fit for her.
Both sets of entrance exams included English, Maths and VR, and Old Palace included some NVR as well.
The interview procedures for the two schools were slightly different. At OP we were interviewed as a family by the Head for about 20 minutes, then DD stayed with the Head on her own for another 20 minutes. They talked about DD's interests, and DD had to answer some reasoning questions and comment on a painting.
At Croydon High DH and I had a brief chat with the Head while DD went with a teacher and two other girls for an assessment in a group. They were given some word puzzles and Sudoko. DD didn't have an individual interview and couldn't remember being asked anything about her interests.
DD was offered an academic scholarship with an additional award for maths at OP, and a place but no scholarship at CH, so we went for OP and have been very pleased with our choice. The pastoral care has been excellent, DD settled in quickly and is very contented.
Good luck with your choice - PM me if you like