Two very different looks from the same job. An inset stove sits back into the chamber and reads as a fire in a wall, which suits a clean modern breast with a large slate or stone panel around it. A freestanding stove sits out on the hearth with air all around it, throws heat from every surface and looks the part in a traditional room. The right answer depends on the breast you have, how much heat you want in the room and the look you are after.

Set back into the chamber with the surround detailed tight to the appliance, for a flush contemporary line.
Standing clear of the chamber so heat radiates from every face, with the flue pipe visible as part of the look.
Straight advice on how much of the heat you actually get in the room from each type, before you choose on looks alone.
Manufacturer distances to combustibles, sides and rear applied to both, which is what dictates how tight the chamber can be.
A freestanding stove, generally. It has air moving over the top, both sides and the back, so it radiates and convects into the room from every face, and the visible flue pipe gives up heat too. An inset stove is surrounded by masonry, so more of its heat goes into the chamber, and good inset models compensate with a convection air path. If maximum output into the room is the priority, freestanding wins.
No. Inset appliances are designed and tested for it, with the correct convection routes and clearances for sitting in a chamber. You cannot simply push a freestanding stove back into an opening and call it inset, because the clearance to the sides and rear are part of what keeps the surrounding masonry and any combustibles at a safe temperature. We fit whichever type the room suits, and we will not fit the wrong one.
Freestanding, most of the time. A cast iron stove standing on a slate hearth under an oak beam with the flue pipe on show is the look people picture when they think of a woodburner, and it sits naturally in a Victorian or Edwardian terrace. Inset units read as contemporary and tend to work best in a modern room or a full breast panel treatment.
A deeper one, usually. An inset appliance needs the chamber depth to take the body of the stove plus the clearances behind and to the sides, and on a shallow breast that can mean building the chamber out or cutting further back into the breast. We measure the existing opening against the chosen model at survey, because it is the single thing most likely to rule an inset out.
It is possible but it is a full rebuild of the chamber, not a swap. The opening size, the depth, the hearth arrangement and often the flue connection are all different, so budget for it as a new installation rather than a change of appliance. It is worth thinking it through properly the first time, which is what the survey is for.
Where the structure allows it, yes. A double sided stove sitting in an opening through a breast between two rooms is a striking thing and a more involved install: the opening has to be formed through the full thickness, both hearths have to comply, and the clearances apply on both faces. It is a survey job before it is a quote.
Send a photo of the chimney breast and David will come back with a price.