Vinyl pergolas
Pros:

Virtually maintenance free
Durable
Rarely crack or split
Don't need to be painted
Don't sink or warp
Easily cleaned
Looks new for years
Moving a vinyl pergola is not hard
Vinyl is immune to bugs

Cons:

They Are Cookie-Cutter
Expensive
Finding Replacement Parts Can be Difficult
Light weight - must be securely anchored
Vines don't stick to vinyl as they will to wood

Wood Pergolas

Pros:

Wood gazebos look classy and traditional
TheyâÂÂre typically gorgeous
You can easily alter the colors with oil-based stain.
More style options with wood
Wood is more durable
Wood blends better with the landscape

Cons:

Wood requires a fair amount of maintenance
Wood needs to be cleaned, stained, and treated to keep them in good condition
Chemicals in treated wood can poison and kill some plants
Wood can warp, split and splinter over time
Wood welcomes termites and other kinds of critters
Depending on size, once secured in place, they are too heavy to relocate

That is quite a comprehensive response. Thank you kayjones!