Obviously the prep school will encourage you to stay on the extra two years paying their fees.
I guess it depends on the senior school whether 11 or 13 is better.
Example:
"Boys wishing to enter the School at 11+ take the 11+ entrance examination in January of their Year 6. Boys wishing to enter at 13+ from preparatory schools also take the 11+ exam in Year 6 for a conditional offer confirmed by a satisfactory pass in the 13+
Scholarship or Common Entrance examinations two years later (see below)."
Which strikes me that you might as welll just pass the 11+ once, rather than do two sets of exams.
This is reflected in the admissions numbers: 75-100 in Year 1 and 50-75 in Year 3.
The Year 3 papers do sound harder as well.
I wonder if perhaps 11+ entry is easier if your child is shy, as a timid child would perhaps be entering with a cohort of similar 11 year olds, as against 13+ entry intermingling with children who have been established for 2 years already plus confident prep school graduates.
I would think from an academic point of view the 11+ entry would mean you would spend Year 7 + 8 doing work that was directly relevant to Years 9-13, than if your child was still at prep school.