All depends on whether the set can handle 1080p content or not. The best HD Ready sets - like the Panasonics and our Pioneer product of the year - will take the Full HD content and automatically downscale it to suit their resolutions.
With other, typically (though not always) cheaper sets, you need to set the player to output at the lower resolution.
For example, see the 26in TV Supertest in our current issue where we mention the sets that do and don't handle 1080p natively. The big surprise is the Sony, which doesn't... (hello, Blu-ray???)