I wouldn't call advertising ‘competing’—I would hope that your advertising is complementing and enhancing your messages.

The best way to isolate the impact of advertising is to manage the timing. For example, Southwest Airlines will launch in a new city with PR first, and measure how many tickets they sell via PR. Then, after a month or so of PR only, they'll add in advertising and measure the results of that.

Another, albeit cruder, way to isolate PR’s impact is, when you are surveying an audience, ask them how much news they get from various sources. If your advertising is on TV and they rely mostly on print for information, chances are that PR is impacting them more than TV. -KDP