This design would have equal level of difficulty in each of the apps mentioned: ID IL or PS. And the answer would be the application you feel the most comfortable using.
If I were to do this in Indesign, I would create layers for each concentric row of photos. The photo frames would not need to be perfect pie slices, rather a rough polygon. The top most layer(s) would be the concentric circles, with white stroke, no fill. And, a top layer for the sectional parts. These would define the pie slices.
This is a quick sample.
1- Draw a circle, then use scale tool to scale about 60% and click on copy,then select the next circle and again scale tool and scale about 90% and click copy. Repeat for others circles.
2- Select the outside circle and next one, and from pathfinder click subtract. Repeat for others circles.
3- Draw a rectangle, then use rotate tool, insert angle for my sample (40) and click copy and from object menu>transform again>transform sequence again.
4- Select all rotated rectangles and circle underneath, from pathfinder click subtract. Repeat for others circles.
5- Select all circle, from object menu>path>release compound path.
6- File>place images.
7- For Type, draw a circle and use Type on a path tool (Shift+T)