For two SQL queries of the same complexity, one in a parallel database scenario and one in a distributed database scenario, which $($if any$)$ should take longer to optimize and why?

The query would take longer to optimize on a distributed database. Because different machines have different performance power, network performance is likely to be slower and may vary across the system, and some data sources might only be accessible from certain machines.

The query would take longer to optimize on a parallel database because each node is homogenous and connected to a large global storage system, which is inherently slow due to its size, and any complex query will take considerable time to process.

It depends on how the query is written.

There should not be a difference in the query processing time if the complexity of the queries is equivalent to each other.