Hi Tommy,
There are few big differences between two method.
From your point there is only difference with the latest method ExecuteRestWebService(1311) are
1. It support other HTTP operation like POST, PUT and DELETE. using these service you can create/update new instance in external system.
POST for Create, PUT for Update, and DELETE for delete instance.
2. previous method ExecuteWebService (1308) does not have all these feature it only support GET operation for RESTfull webservice based on JSON. You can use POST operation in mashup webservice and provide the data in Body* but this is only support XML based communicaton not JSON.
If you want to Read data(GET) from external system you can use any of method, both will work in a same way.
(using mashup webservice for GET is more comfortable than ExecuteRestWebService(1311)).
In order to parse JSON response still a tedious job, and also it seems less feasible for huge data.
SAP should have provide a proper parser for JSON. In one blog of Thomas he has given very good idea to parse JSON. Please check the below link for more details.
http://scn.sap.com/thread/3427857
http://scn.sap.com/thread/3402558
some few point about mashup webservice ExecuteWebService (1308) :
1. for using method ExecuteWebService (1308), You have to create mashup webservice, which main purpose is providing connectivity and data access from external system to mashup, embedded on your screen.
2. It does not support RESTfull webservice in mashup. (for example in data mashup you can not use mashup webservice)
I hope that SAP is still working on this functionality and in future we will have better functionality for using RESTfull webservice based on JSON.
Thanks
Sunil