The Jazz's perimeter defense used be bad because our interior defense was so weak (Boozer/Okur) that it required one or two players to collapse and help out in the paint, leaving their man on the wing. Jerry Sloan used to do this on purpose for years--have one of the guards go double team the post in an effort to dig the ball out. (This is how John Stockton got a lot of steals.) But having one of the guards help defend the paint left a shooter open on the perimeter, so opposing teams could swing the ball around and get an open look.
Now with Favors in the middle, the interior defense should be better, so we shouldn't have to collapse as much. If we're still getting burned on the perimeter, it's probably because our guys aren't quick and tenacious enough as on-the-ball defenders. In the Philly game, Lou Williams and Jrue Holiday (to a lesser extent) could get by Harris, Bell and Hayward because they were quick and crafty off the dribble. The Spurs, meanwhile, are one of the best teams in the league at spacing the floor. They have a quick PG in Parker who dives into the paint, and they have good shooters waiting for the kick-out. They're just a tough team to play, and their offensive schemes still work. It's just that they aren't as good defensively as they were when they were winning championships.