Runscope covers all of your three requirements, and then some, especially in the history department. All of the requests you make using Runscope are stored, full request/response with URI, headers, etc. They're also indexed and tagged, so you can free text search the payload, by host, by status/error code, etc.
In response analysis, you can also place two requests side-by-side and compare them diff style. See a demo screencast here.
What's more, you take any request from the log, and convert it into a Runscope Radar automated test that runs from the cloud, complete with assertions (i.e. validate response code, content in the payload, etc.)
Note: I work for Runscope. That being said, I'm also a developer that has used Postman and SoapUI extensively. Both swell tools in their own right.