I believe Require-Bundle is an Eclipse thing (that has now made it in the OSGi spec to accommodate Eclipse). The "pure" OSGi way is to use Import-Package, as it specifically decouples the package from the bundle that provides it. You should be declaring dependencies on functionality that you need (the Java API provided by a certain version of a certain package) instead of where that functionality is coming from (which should not matter to you). This keeps the composition of bundles more flexible.
JavaScript analogy: This is like detecting whether a web browser supports a certain API versus inferring from what the user-agent string says what kind of browser it is.
Peter Kriens of the OSGi Alliance has more to say about this on the OSGi blog.
Probably the only case where you need to use Require-Bundle is if you have split packages, that is a package that is spread across multiple bundles. Split packages are of course highly discouraged.