In developing NoSQL databases, a major motivation is to achieve better efficient query performance compared with relational databases. The graph database is a NoSQL paradigm where navigation is based on links instead of joining tables. Links can be implemented as pointers, and following a pointer is a constant time operation, whereas joining tables is more complicated and slower, even in the presence of foreign keys. Therefore, link-based navigation has been seen as a more efficient query approach than using join operations on tables. Existing studies strongly support this assumption. However, query complexity has received less attention. For example, in enterprise information systems, queries are usually complex so data need to be collected from several tables or by traversing paths of graph nodes of different types. In the present study, we compared the query performance of a graph-based database system (Neo4j) and relational database systems (MySQL and MariaDB). The effect of different efficiency issues (e.g., indexing and optimization) were included in the comparison in order to investigate the most efficient solutions for different query types. The outcome is that although Neo4j is more efficient for simple queries, MariaDB is essentially more efficient when the complexity of queries increases. The study also highlighted how dramatically the efficiency of relational database has grown during the last decade.