It definitely depends upon the art
Normally I deal with charts and graphs that were done in Photoshop or Illustrator. I do the Figure Titles and captions in InDesign and group them with the art/graph. But the figures and axis points itself are done in Photoshop or Illustrator.
That is because while we may have to adjust the size of the art itself, we want the figure title and captions to always be the same size.
What kind of charts are you talking about? Similar to Excel charts and graphs, or tables that could be done in Indesign? If more of a table, then I’d do the table in InDesign with the background behind it.
I guess one way to look at is what has the best chance of needing to be edited? It’s much easier to edit a caption or table in InDesign. If you have to do it in Photoshop, then you need to edit it, then update the art in InDesign. So it’s a two-step process.
But that’s just me. I’m sure others here will have different opinions and reasons why.