This is a good question - but I don't think you can answer without bringing Blackfish into the debate, and the book Death at Seaworld, as they are hugely informative.
I definitely have a problem with orcas in captivity as research has shown that they are hugely intelligent, emotional animals who have reacted very, very poorly to being in captivity. They are not natural killers but if you see any of the attacks they have made on humans, they are very deliberate and calculating attacks, not simply lashing out, which in itself shows a high level of intelligence. There is one attack in particular on a trainer which was caught entirely on film where the orca was deliberately taking and rolling its trainer underwater but not for long enough to kill him, and this went on for about 10 minutes. The evidence to me seems quite clear that orcas are as stressed to being in captivity as a human would be, and their behaviour becomes very unnatural and deliberately violent.
The use of captive animals as entertainment I also find distasteful to the point of being upsetting.
Watching Blackfish has also made me question zoos. I want to do more reading about it. I believe some animals can be kept in captivity in environments which are almost identical to their natural environments, and their behaviour and quality of life doesn't suffer. But for other animals, larger animals, or more intelligent animals, they probably do feel as though they are captive, and that is wrong.
Though that captivity does need to be balanced against endangered species where captive breeding programmes are keeping them alive.
All round I am less happy about zoos than I was before I watched Blackfish.