Klefbom was great 3 years ago, but since then he's been up/down. -17 last year was by the worst on the Oilers D last year, and no he's doesn't play the top defensive minutes. He's third on the D for 5-on-5 minutes behind Nurse and Bear, the reason his ice time is sky high is because the Oilers employ basically just 1 unit on the PP and he gets all the d-man time on the PP.
Barrie is honestly probably the better player, more talented certainly. Other teams fans take for granted things like the offence Giordano, Hughes, Reilly bring to a team, but when you don't have a dynamic offensive D in the modern NHL it is a massive bottleneck in your team's ability.
Nurse basically plays the same role as Klefbom as the "all-around" jack of all trades, master of none type player that Klefbom is, but the Oilers haven't had a top end offensive D that can actually make a play with the puck for ages. All our current D either freeze up when McDavid or Draisiatl give them a glorious chance with time and space, or are too raw (Bear, Jones) to really properly capitalize.
The other thing that I think benefits the Oilers is their young D aren't that young. Bear and Jones are not like 19/20 year olds being rushed into the NHL, they're both 23 turning 24 next year. That's a fairly large difference.