The Golf Umbrella

Pros:

Bigger canopy provides more coverage from the rain.

Some models have two canopies, which help prevent them from flipping inside out on windy days.

Some are made from sturdier materials, such as steel or fiberglass.

Cons:

It's big, making it a pain to lug around and an object of derision for anyone walking near you.

Often pricier than your average umbrella.

The Folding Umbrella

Pros:

Smaller and more portable than a golf umbrella.

Some have automatic open and close buttons.

Cons: 
Flimsier than a golf umbrella, though some makers are experimenting with sturdier.

The Mini Umbrella

Pros:

So tiny it can fit into a small purse.

Cons:

With more parts than a regular folding umbrella, it is very prone to breaking.