What are the pros/cons for choosing a style for dormers? I'm not asking about the aesthetics of one over the other, more a comparison of the construction costs, maintenance costs, and any other reliability concerns.
There are a few considerations to cost, I don't consider reliability to be a major factor in either style of roof. Dormer and shed style roofs have been used for many hundreds of years successfully. The main choice for either of these is aesthetics, and simplicity of assembly.
First, if you have to deal with a large snow load it is cheaper and easier to go with a peaked roof. The size of members required in a shed roof of any size with a significant snow load is prohibitive.
I believe that it is slightly more cost effective to go with a shed style roof. You have less material required to finish the roof due to less surface area. If your span is not too large you can get away with laying boards across your walls and not having to build trusses. In the end this is possibly slightly more difficult to construct properly though, great care has to be taken to ensure the landing points of your load members meets the walls well and it can make for some interesting finish work.
With the shed style, you have fewer intersections to worry about so statistically you would have a lower risk of leaks. But if a quality contractor does the construction of either style, then you don't have worry about this being a problem.
Depending on the construction of the roof, a shed style dormer might not be possible. It's also possible you might not be able to install any type of dormer.
In terms of cost, no one here is going to give you an answer. It's impossible to know. You should find a local contractor to give you an estimate.