(This is abbreviated text from The Global Indie Author.)
The advantages to owning your ISBNs are:
Increased Distribution Options
Most vanity publishers and aggregators have limited distribution partners (often only one for print and maybe a half-dozen for ebooks). If you own your ISBN you can contract with as many wholesale distributors as you wish including Lightning Source, which is owned by Ingram, is U.S.-based and has two international subsidiaries, has an extensive list of distribution partners, and gives you access to the libraries and academic markets as well.
If your book is published by any of the known vanity publishers or aggregators, everyone will know your book is self-published. If, on the other hand, you create your own imprint, it is not necessarily apparent that your book is self-published. While at first this might be nothing more than semantics—and with only a modicum of digging the gig will be up—over time you can build your brand.
Books in Print
Having your own ISBN means you control the information available through Bowker’s Books in Print. This is done through the MyIdentifiers website. It is free to sign up and is available to all authors who own their ISBNs, including foreign authors with foreign-issued ISBNs.
Free National Agency Advertising
Finally, owning your own ISBN means you can take advantage of free pre-release advertising (if available) via your ISBN registry. Library and Archives Canada, for example, has a program called Cataloguing in Publication whereby in advance of publication publishers can voluntarily make available to LAC information such as the intended date of publication, the title page, list of contributors, genre and primary audience, your book description, and its table of contents and preface (if applicable). This information is then disseminated to libraries and retailers via the New Books Service, an on-line service showcasing new Canadian publications; via the national bibliography Canadiana; LAC’s bibliographic database, AMICUS; and in Canadian Books in Print. The intention of the program is to provide advance promotion for publishers and to assist booksellers and libraries to plan their purchases. It is not currently available for ebooks and is limited to print books with an intended initial print run of 100 or more copies. The Library of Congress has a similar program.
And the Disadvantages
The first and most obvious disadvantage to owning your ISBNs is the expense if you live in a jurisdiction where you have to pay. This can be reason alone for many indie publishers to accept an ISBN from their digital aggregator or POD/vanity press company.
The second disadvantage is that you, as the publisher, are legally responsible for fulfilling the requirements of Legal Deposit both in your own country and additionally to the Library of Congress if you are a foreign publisher distributing in the U.S. This is an additional task and expense.
The third disadvantage is that you have to do the work. You have to sign up for the account, keep track of your ISBNs, and input and maintain the information in the Books in Print or similar database(s).
If you and the publisher are one and the same, meaning your publisher address and phone number are also your personal address and phone number, your personal contact information will be available to anyone with a subscription to the Books in Print or similar databases (mostly libraries and retailers). So if you are concerned about this—if you intend to publish a book you believe may be controversial, for example—then it might be better to use a vanity publisher or aggregator’s ISBN. The thing about being a writer or any other public figure is that success comes at the expense of anonymity. So if this is an issue for you, write under a pen name and then either legacy publish, vanity publish, engage the services of an aggregator, or e-publish only without an ISBN. You can also elect to set up a separate company for your imprint, with a third party such as a law firm listed as the contact information.