Outside, every time, and the reason is simple enough to be worth stating plainly: a blind on the inside of the glass stops the sunlight after it has already become heat in your room. A shutter outside stops it before it arrives.
There is a piece about external shutters and shading which goes through the detail, including the part people do not expect, which is that the same shutters help in winter by cutting heat loss through the glass at night.
What the site does not have, and will not invent, is a percentage. The figures quoted around the internet for how much a shutter cuts solar gain vary enormously depending on what was measured and where, and putting one here would be pretending to a precision this site has not got.
If you have fitted either, what changed in the room and roughly what it cost is exactly the kind of thing this forum is for.