"Generic" describes as being non-specific. When defining genre, a generic song wouldn't qualify as pop, rock, rap, country, or what have you because a generic song doesn't fit a specific genre. Depending on what you're trying to qualify, generic might be describing something different, such as mood or activity, instead of genre. When describing music, it would have a negative connotation, implying the music doesn't have any particular qualities that stand out.
"General" means it applies in most cases. If there's a song you like to listen to regardless of mood or activity, then calling it a "general song" would be appropriate.