Process-Aware Information Systems (PAIS) is an IT system that support business processes and generate large amounts of event logs from the execution of business processes. An event log is represented as a tuple of CaseID, Timestamp, Activity and Actor. Process Mining is a new and emerging field that aims at analyzing the event logs to discover, enhance and improve business processes and check conformance between run time and design time business processes. The large volume of event logs generated are stored in the databases. Relational databases perform well for a certain class of applications. However, there are a certain class of applications for which relational databases are not able to scale. To handle such class of applications, NoSQL database systems emerged. Discovering a process model (workflow model) from event logs is one of the most challenging and important Process Mining task. The $α$-miner algorithm is one of the first and most widely used Process Discovery technique. Our objective is to investigate which of the databases (Relational or NoSQL) performs better for a Process Discovery application under Process Mining. We implement the $α$-miner algorithm on relational (row-oriented) and NoSQL (column-oriented) databases in database query languages so that our algorithm is tightly coupled to the database. We present a performance benchmarking and comparison of the $α$-miner algorithm on row-oriented database and NoSQL column-oriented database so that we can compare which database can efficiently store massive event logs and analyze it in seconds to discover a process model.