No, I don't think that Kidd necessarily puts the Spurs on the Lakers' level, although it would be a great step in that direction.
The Spurs need at least one more clear offensive threat (at whatever position), someone who averages 16ppg but can be a threat to go for 25 when needed. Maybe that player will be Ginobili, but if not they need to acquire a Wally, Rashard, Richard Jefferson or Rip type via free agency, or via a trade for Parker and change.
Also, they'll need one more quality big man, either a C or PF who can be a reasonably skilled, complementary big body to do a few things to distract some attention from Duncan. Doesn't have to be a superstar, but even someone on the level of Brad Miller, Brian Grant, etc.
And then of course they need the rest of the role players, guys who know their place and get the job done. Some of those guys may already be on the roster, like Bowen.