I agree with the people saying that its subjective and really depends on the genre. Hes not astounding or legenadary as a drummer but like Freebase said he keep a rhythm right on point and fits his mold well.
And I think it was Big3 who mentioned this but alot of people really dont many drummers by name or off hand but if you mention Barker most people will immediately know who your talking about. Say if you mention some guys like George Hurley, Bud Gaugh or Mitch Mitchell it may not sound so familair haha
People tend to forget this but he(Barker) was also in The Aquabats for a short period.