For perpendicular parking, it either works or it doesn't, for the most part. I cannot recall a case when it tried to park my car in a perpendicular space and really messed up. I might quibble with how it spaced the car but no collisions that I recall. More often, it won't try because, as others said, there are no adjacent cars or other obstacles to guide by.
Parallel parking at the curb is a different story. Way back in the early days of AP1, the car struck the curbs twice during parking, and gave two wheels some curb rash. Very unsettling. But I have not had a similar problem in the past 2 or 3 years.
As a retired person, i do not get to use either type of parking very often, so my data set is not very large.