Refer the below link for your reference.

Should it be a WebAPI or asmx

Web Service (.asmx)

• It is based on SOAP and return data in XML form.
• It support only HTTP protocol.
• It is not open source but can be consumed by any client that understands xml.
• It can be hosted only on IIS.

WCF (.svc)

• It is also based on SOAP and return data in XML form.
• It is the evolution of the web service(ASMX) and support various protocols like TCP, HTTP, HTTPS, Named Pipes, MSMQ.
• The main issue with WCF is, its tedious and extensive configuration.
• It is not open source but can be consumed by any client that understands xml.
• It can be hosted with in the applicaion or on IIS or using window service.

Web API

• This is the new framework for building HTTP services with easy and simple way.
• Web API is open source an ideal platform for building REST-ful services over the .NET Framework.
• Unlike WCF Rest service, it use the full feature of HTTP (like URIs, request/response headers, caching, versioning, various content formats)
• It also supports the MVC features such as routing, controllers, action results, filter, model binders, IOC container or dependency injection, unit testing that makes it more simple and robust.
• It can be hosted with in the application or on IIS.
• It is light weight architecture and good for devices which have limited bandwidth like smart phones.
• Responses are formatted by Web API’s MediaTypeFormatter into JSON, XML or whatever format you want to add as a MediaTypeFormatter.

Reference: StakOverFlow