The 1958 has similar tail fins to the 1958 Chevy Impala where they go up and out slightly.
The 1959, again is like the Chevy Impala, but this year both had tail fins that stuck up vertically - more-so than the Chevy, but were noticably larger fins than the 1958.
Here are a couple links to see the visual differences between the two.
The 59s were the first of the modern Bonnevilles. That was a the first year for the famed 389 and wide track. The Wide track was to make the cars tires look better on the car but they soon found out it helped the cars handling. The 59-60 was the last of the Harley Earl look then came the clean look from the Bill Mitchell studios.