Better handling, reduced braking distance, maybe a slight mileage hit. All of course, depends on tire model selected. I have used both 205's and 195's GY TTT's with great results.
+1 Note that when Consumer Reports road tested the Standard Prius with its 185/65R15 tires and the Touring Prius with its 195/55R16 tires, it found that the Touring Prius got 10 - 12 feet shorter 60-0 mph stopping distances. I think that most if not all of this was due to the 195 mm tread width of the Touring tires.
When I bought new tires I went to the 195/60 R15 and the handling, stopping, and cornering difference is worth it. I have averaged 58 MPG tanks all spring and summer compared to last year I was averaging about 61 MPG (on worn out Integrities) So the mileage drop is not significant.