Tom's answer is quite detailed and exhaustive but you may also be interested in this simple study about Parquet vs Avro done at Allstate Insurance, summarized here:
"Overall, Parquet showed either similar or better results on every test [than Avro]. The query-performance differences on the larger datasets in Parquet’s favor are partly due to the compression results; when querying the wide dataset, Spark had to read 3.5x less data for Parquet than Avro. Avro did not perform well when processing the entire dataset, as suspected."