APIs demonstrate critical importance for client-server communication because of fast web and mobile application development. REST and GraphQL serve as dominant API architectural styles which exhibit different operational characteristics. REST maintains its position as a core choice for simple and scalable development but GraphQL delivers higher flexibility to specify data queries. The performance evaluation of REST and GraphQL APIs uses response time along with CPU utilization and memory usage metrics as their analytical framework. The research implements experimental evaluations together with comparative studies to identify their performance trade-offs while defining their best application scenarios. The outcomes of this study guide developers together with architects and decision-makers in choosing the right API standard when applying specific application specifications along with system limitations.