I have to choose between custom data tags or ids. I would like to choose custom data tags, but I want to be sure that they do not cause browser compatibility issues for the most
I would advise in favor of data attributes for the following reasons:
and probably less relevant in your case:
However, I'm not sure whether I understand your specs completely as extracting the element id in jQuery is as trivial as getting the data attribute: $('.foo').attr('id');
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You might be interested in Caniuse.com, a browser compatibility site for web technologies.
If XHTML is an issue to you, you might also be interested in how to use custom data attributes in XHTML: see here for a discussion on SO and here for an XHTML-compatible approach using namespaces.