Question: Should my profile be specific or general?

It depends on what you want. If you are 100% clear about the position you want, in a particular industry or type of company (small or big, consulting or corporate, etc.), then BE SPECIFIC.

If you are undergoing a career change, then be general and only stress your core competencies (e.g. leadership, project management, self-motivation, etc.) without mentioning skills that are too specific (Oracle database, direct marketing, etc.).