But Mr Busch has denied such abuse, saying it is "very untrue".
"My animals are the happiest animals you will ever see on this planet, and when you see them you can not fault that," he said in an email statement to NZME. News Service.
Accusations that he declawed Jabula were "also untrue", Mr Busch said.
"I'm sure Jabula would like to show him [Mr Berrange] his claws," he said.
Mr Berrange was part of a "smear campaign" against him, Mr Busch said, sparked by jealousy following filming of a documentary together.
"I filmed two episodes with him, I also invited him to England as a guest speaker at an event ... he sat with me at a table to do autographs for my fans," Mr Busch explained.
"I had a large line of people wanting to meet and have autographs. I could see this made him very envious and jealous. It was very obvious he wanted what I had, which was a TV program and fans."
When they returned to South Africa, Mr Berrange tried to pull out of the documentary, asking for all the footage of him, Mr Busch said.
He decided to put the footage "on the shelf for various reasons", one of which was a disagreement over Mr Berrange's methods for catching leopards, Mr Busch said.
"It is very cruel from what I have seen and have on film. These tactics of his ruined these leopard's lives. I do not want any part of that."
Louise Joubert, founder of Sanwild Wildlife Trust, told South African newspaper Rapport that she was critical of Busch's plans for the sanctuary, saying it was "unnatural to tame wild animals".
Mr Busch said he did not know Ms Joubert, but understood that the trust was "not part of the conservation family".
"They are animal activists and in general they don't support Government policies in terms of conservation management in South Africa," he said.
In a separate email, Mr Busch said a long-running smear campaign had been orchestrated against him by his "so-called mother and others around her that want to steal the park and now my cats in New Zealand, and also the Lion Man brand".
"This is why I don't live in NZ ... I don't want to live around that sort of carry on and be a pawn to them," he said.
Mr Busch rose to fame as New Zealand's Lion Man with a television series in 2004 based at Whangarei's Zion Wildlife Gardens.
In the decade since, there has been a lengthy and costly legal battle between Mr Busch and his mother Patricia Busch over control of the park.
In May 2009, big-cat handler Dalubuhle Ncube, also known as Clifford Dalu Mncube, or Dalu, was mauled to death by a male tiger named Abu after he and another handler entered its enclosure to clean it.
The park was reopened and renamed the Kingdom of Zion in 2012. It has since changed hands and become the Kamo Wildlife Sanctuary, run by investment company Bolton Equities. It is currently closed for upgrade work to meet new rules around animal enclosures.
It is understood Mr Busch intends to move between four and eight of the 34 big cats held at Kamo Wildlife Sanctuary to his new sanctuary in South Africa.