Barker, who won an IBF middleweight title, said: "Wladimir Klitschko has been the standout heavyweight for a decade and it would be exciting to see how our young standout Anthony Joshua would go against him.
"But after watching Parker there, how hungry and ambitious he is, how spiteful he looks, it's a very interesting division at the moment. After seeing Parker I'm not sure which fight I would look forward to seeing most."
Oliver said Klitschko would be the safer bet for Joshua.
"As a calculated gamble, you would go with Klitschko after his poor performance against (Tyson) Fury, but that was only one poor performance and we don't know what he's got left," said Oliver.
"That's the best heavyweight top 10 I've seen in years - every one of those guys can fight. Parker is a real danger and improving all the time.
"We speak to Anthony Joshua on a regular basis and he's hungry for the big fights. Hardcore boxing fans would want Parker - he's young, fresh, he brings something dangerous to the table.
"You know you would get fireworks with those two trading off in the centre of the ring. It would be explosive and could end early either way.
"Klitschko is the bigger name and that would be more appealing to the general public. He had one terrible fight against Fury when he barely threw a punch, but before that he showed no signs of deterioration."
Both rated the 37-year-old Cuban Ortiz as the most dangerous contender and "the man to stay away from".
Their top 10.-
1) Tyson Fury
2) Wladimir Klitschko
3) Deontay Wilder
4) Anthony Joshua
5) Alexander Povetikin
6) Joseph Parker
7) Kubrat Pulev
8) Luis Ortiz
9) David Haye
10) Andy Ruiz
