Type 1
The Type 1 Tuned Mass Damper consists of a cylindrical ring of steel mass, which is suspended by cables.  The ring is larger than the diameter of the stack, and is separated from the stack with coils of cables which serve as springs. 

Advantages: 1) All Mechanical Parts 2) No problem with high temperatures 3) Inspected from grade with Binoculars 4)  Provides large structural damping

Disadvantages: 1) Must be full 360 Degrees 2) Needs to be near top of stack. 3) Can not serve dual purpose (i.e platform)

Type 2
The Type 2 Tuned Mass Damper is also referred to as the "roller box" damper.  It is a completely enclosed damper with a mass which is rolling on the inside of the damper shell.  It is suited for small stacks with small accelerations. 

Advantages: 1) Inexpensive 2) No problem with high temperatures 3) Completely enclosed 4)  Suited for small stacks and small accelerations

Disadvantages: 1) Must access damper for inspection. 2) Needs to be near top of stack. 3) Can not serve dual purpose (i.e platform)