Here is my take, I am sure I missed a few pros and cons for both, but should sum it up.
Chassis pros
- drop in fit
- generally don't require bedding
- don't require bottom metal
- solid platform
- generally less cost over fiberglass (bottom metal, inletting, bedding)
- many designs to choose from
Chassis cons
- heavier than fiberglass
- cold in cold weather, hot in hot weather
- not as "traditional" of a feel
- not as snag free as a solid fiberglass stock
fiberglass pros
- light weight
- solid platform
- not as temp sensitive to the shooter as aluminum
- can be modified for different action/bottom metal at a later date
- often offer better texture in the grip and forend area
- great for positional shooting
fiberglass cons
- requires smith fit (inletting, bedding, etc)
- requires bottom metal
- generally costs more than chassis
- more potential for manufacturing errors
With the above list of pros and cons for each as I see it, when choosing a chassis I always opt for a folder. I feel its one of the biggest benefit to a chassis, you gain weigh but have a more compact rifle for packing. I go between fiberglass an chassis systems and own and use them both, I like the traditional feel of fiberglass as well as the more basic design, especially for positional shooting, but the chassis is a very stable platform and offers a lot of bolt on adaptability (rails, etc) that most fiberglass stocks do not.