Strangely, I have experience of both within the last 3/4yrs. I'm not a builder, so I'm far from any expert, but some things I've learnt as a general home owner.
My understanding is that a conservatory has more glass and a pitched type roof, whereas an orangery has more brickwork, flat roof and often a lantern in the middle.
Conservatories/orangeries within a certain size are generally allowed without planning under permitted development.
1 thing is they expect a door between the conservatory and the main house.
Property 1
We didn't want a closed door between the conservatory and main house, because we wanted it to be more extension like. We wanted more space in the kitchen/diner. Not just a room shoved on the end of the house behind a door. We also installed a small cloakroom. We approached 3 conservatory companies and none had heard of adding a toilet before nor removing the door between the main house! Several suggested we keep a door and once they'd left, we could remove it ourselves and do what we liked! You'd need building control to check it if you go for the no door option like we did.
This build was complicated, and FAR more expensive, by it being over a sewer pipe and wrong information from the conservatory company.
It was maybe 4m x 5m. We chose the best UV glass available, 1 entire wall was brick, and we had brick about 1m up each wall. I don't recall details of what insulation they put in.
We were only there a few months after completion before we moved for family reasons. It did feel very hot and bright in sunny weather, but better blinds would have helped.
Property 2 (current house)
This was a re-build of what had been a derelict extension and a cross between an extension and orangery. It has new, full height brick walls like a normal room, but due to the amount of large windows, bifolds and large lantern, might technically be an orangery? It too gets very hot on sunny days, but we have thermal blinds which help. We also have 4m bifolds which we open to release the heat. This was part of a much larger renovation, so I can't give prices of just this part.
Currently, this room is used for indoor plants, growing seedlings and storage boxes because we are still renovating. It might be a games room/bar in future. The lantern seems to collect a terrible amount of flying insects which I didn't consider.
I'm sorry this is long and I'm not sure I've helped. Maybe just some things to consider though.