Is a rigid gazebo roof less likely to be damaged by wind than a fabric roof?
Structurally, the fabric will put more stress on your gazebo than a fixed panel for two reasons: 1) When the fabric “snaps” from the thrust of the wind, it creates an IMPACT load, and 2) A fixed (rigid) panel will DISTRIBUTE the load to other structural members.

Likewise, something that flexes and moves will tend to “wear” more than something that does not. Maintenance will be more in the long run. 

For just simple enjoyment of the space, I’d think a rigid “roof” would be quieter too...best for conversations.