What an inside mount buys, and what it costs
An inside mount sets the shade in the window opening, so the trim around it keeps doing its job. On a house with generous casing, that matters. You paid for the millwork. An inside mount lets you see it. The shade also reads as part of the window rather than as something hung on the wall, which is why it photographs well and why most of the images saved to your inspiration folder are probably inside mounts.
It asks for three things in return.
The first is depth, which is the whole conversation. The headrail has to fit behind the face of the frame with room left to operate, and how much depth that takes varies by the shade. Cellular shades want the least. A roman, with a fabric roll and a lift system inside the headrail, wants the most. If the window does not have it, no amount of wanting it changes the answer.
The second is a light gap. The workroom takes a small deduction off the width so the shade clears the frame on both sides without dragging, and that deduction shows up as daylight down each edge. In a kitchen at two in the afternoon nobody notices. In a bedroom at six on a June morning, everybody notices. That is why I ask what room we are standing in before I ask what fabric we are looking at.
The third is a square opening. An inside mount is measured to the opening, so whatever is wrong with the opening becomes wrong with the shade. Windows in older Michigan houses are frequently out of square, and a window that is out at the top and true at the bottom hands you a shade with a wedge of daylight down one side and nothing to hide it behind.
There is a fourth item that is really a subset of the first. A shade stacks when it is raised, and inside the opening that stack sits on the glass, so on a short window you can lose a surprising amount of view to a shade that is technically open. On a window 34.5 inches tall, that is worth working out before the order goes in rather than after it hangs.
What an outside mount buys, and what it costs
An outside mount hangs the shade above the opening, on the casing or on the wall, and it fixes the things an inside mount cannot.
It covers an out of square opening, because it was never measured to that opening. It blocks more light, because it overlaps the frame instead of sitting inside it. And it changes a window's proportions: mount it higher than the opening and the window reads taller, carry it wider and a small window stops looking small. On a kitchen window with a run of cabinets on either side, that flexibility is worth a great deal.
What you give up is the casing, and that can be a real loss rather than a technicality.
The other thing an outside mount asks for is intent. One that overlaps the casing by a hair looks like a mistake. One mounted well above the opening and carried past the trim on both sides looks like a choice somebody made. Same shade and same window, with different instructions going to the installer, and you can see the difference from the doorway.
It also needs a flat, solid surface to land on. Between the casing and the wall above it that is usually straightforward, but it is worth confirming at the window rather than on paper, which is one of the reasons our installer goes out and takes his own measurements instead of working from my email.
So: inside mount when the window will take it and the room can live with a light gap. Outside mount when the depth is not there, when the opening is out of square, or when the window is simply the wrong size for the wall and the treatment is the least expensive way to correct it.
If you have a window in Oakland County that you keep meaning to do something about, send us the room and we will come measure it.