Executive search firms need a good resume from you, but they also must have a search assignment that matches your background before they can be of service. Headhunters do not market you. They find the best candidates for client job openings. Their clients are companies that pay their fee or retainer. Don't expect a headhunter to make you her number one marketing project. Conducting your search campaign isn't her job, it's yours.
Despite conventional wisdom, you do not want to start your job search with a major resume effort. To do this puts the cart before the horse. A resume is really a kind of ad or brochure. Before developing an ad campaign, an advertising agency carefully targets its market and defines its customers' needs and priorities. Only after identifying these factors, does the copywriter describe features and benefits most useful to the targeted market. In your case, you are the product. You bear the responsibility of selling your most important experiences and attributes to potential employers on a person-to-person basis. If you write your resume before you have found out what they need, you are missing an opportunity to present your best case.
If your resume will be read by a resume scanning program for key words, it's absolutely imperative that those key words be included in your text. Consequently, tailoring your resume to an ad, networking recommendation or job description is probably even more important than if a person were doing the initial screening. In this respect people-scanned and computer-scanned resumes are very similar. However, because some computer scanners have difficulty reading vertical lines, italics and unusual type fonts, techniques you might use to grab the attention of recruiters can be misinterpreted by a computer. If your resume is likely to be scanned, keep the format simple and use only boldface type and bullets to highlight major points.