No but it does change based on whether the safety pilot is in fact a safety pilot, which is only when the hood is on.

Read the FAA Chief Counsel's analysis in the recent opinions about safety pilot not being able to log cross country time and see what you think. They are all primarily based on the the fact that a safety pilot is only a required crewmember for a portion of the the flight - when the hood is on the other pilot.

For example.

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Pilot B was a required flight crewmember while acting as the safety pilot, but Pilot B may not log cross-country time for any portion of the flight because Pilot B was not a required flight crewmember for the entire flight
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http://www.faa.gov/about/office_org/...is%20Glenn.pdf

In addition to the result that time builders don't particularly like, the Glenn letter and its companion Gebhart letter are a pretty good review of the safety pilot rules.

http://www.faa.gov/about/office_org/...09/Gebhart.pdf