Which is better to use as an unambiguous and versatile identification number for books, ISBN-10 or ISBN-13? Is there any need for using both?
ISBN-13 is the present standard, so I’d suggest using that. There really is no need to use both.
ISBN-13 started being introduced in 2007. For a time either system could and would be used, especially since ISBNs are purchased and firms had old numbers to burn off. If you had an ISBN-10 number you could convert it to a unique ISBN-13, but some firms made the effort and used both and some didn’t bother. Today, all books should be using ISBN-13 and not 10.
Therefore, the problem is that your question isn’t unambiguous. If you’re talking about all books, you have to use both. If you’re talking about some date-limited subset of books, you use one or the other or neither. A nine-digit SBN was introduced in the UK in 1965 and the ten-digit ISBN-10 in the US in 1970. Before then, an LC number (Library of Congress Card Number), the last two digits in the year plus an index number, e.g. 57-3468, was often seen in books. That system was officially introduced in 1898 although I don’t remember seeing it on pre-WWII books.
Or, to make it short: what did you want to use if for?
All ISBN 10s have an ISBN 13 equivalent (prefix 978 and recalculate the check digit)
But not all ISBN 13s have an ISBN 10 equivalent, as it’s a larger number range - the prefix 979 is set aside for ISBN 13, and no ISBN 13 beginning 979 can be related to an ISBN 10.
In short: use ISBN 13 and forget ISBN 10
There are tools on the web to do this.
When ISBN-13 was introduced I was told that it was because we were running out of numbers and had to make them longer, which isn’t true. It’s so that they conform to the International Article Number.
Most often I want to identify a book from its description on Amazon, to tell a purchasing agent to buy it. I can’t point to a web page, I’m filling out a data entry form with limited defined short fields. As opposed to most other vendors, Amazon has no catalog numbers to cite. They do, however, usually have both ISBN numbers.
It’s sort of true - we were running short of ISBN10s, and ISBN13 allowed the creation of a brand new range - the ones with the 979 prefix.
Both numbers uniquely identify a specific edition of a specific book, so for you either should be fine. If I had to choose I’d say 13, as the use of 10 is dying.