Stainless steel vs. masonry chimney

Hello everyone

I am currently in the construction planning phase.
I am now faced with the decision:
A Swedish stove with a stainless steel chimney, which is supposed to run on the outside wall of the house,
or a masonry chimney with a fireplace insert.

Can you tell me the pros and cons of both,
or rather, I am interested in the price difference between the two.

Thanks in advance for your answers

Best regards Smike

may I use both
I would then adjust the location which I also have at my free disposal where

my main concern is the purchase price (approximately)
of both variants

best regards