REST API provides a powerful, convenient, and simple REST-based Web services interface for interacting with Salesforce. Its advantages include ease of integration and development, and it’s an excellent choice of technology for use with mobile applications and Web projects. However, if you have a large number of records to process, you may wish to useBulk API.
When to Use SOAP API
SOAP API provides a powerful, convenient, and simple SOAP-based Web services interface for interacting with Salesforce.You can use SOAP API to create, retrieve, update, or delete records. You can also use SOAP API to perform searches and much more. Use SOAP API in any language that supports Web services. For example, you can use SOAP API to integrate Salesforce with your organization’s ERP and finance systems, deliver real-time sales and support information to company portals, and populate critical business systems with customer information.
When to Use REST API
REST API provides a powerful, convenient, and simple REST-based Web services interface for interacting with Salesforce. Its advantages include ease of integration and development, and it’s an excellent choice of technology for use with mobile applications and Web projects. However, if you have a large number of records to process, you may wish to useBulk API.
When to Use SOAP API
SOAP API provides a powerful, convenient, and simple SOAP-based Web services interface for interacting with Salesforce.You can use SOAP API to create, retrieve, update, or delete records. You can also use SOAP API to perform searches and much more. Use SOAP API in any language that supports Web services. For example, you can use SOAP API to integrate Salesforce with your organization’s ERP and finance systems, deliver real-time sales and support information to company portals, and populate critical business systems with customer information.
for more detail follow the below link:
http://www.salesforce.com/us/developer/docs/api/Content/sforce_api_quickstart_intro.htm
http://blogs.developerforce.com/tech-pubs/2011/10/salesforce-apis-what-they-are-when-to-use-them.html
http://www.salesforce.com/us/developer/docs/api/Content/sforce_api_quickstart_intro.htm
If you have to ask this question then I would recommend that you use neither.