Hi Derek,
I am in no way affiliated to any lion hunting or organisations directly in SA/Kenya. However I am well aware of differing opinions and organisations within the industry.
In SA you have captive bred hunting. There is vast difference in a proper captive bred lion hunt and what unfortunately has tainted the industry which is known as canned hunting. Almost all organisations are against canned hunting, whereas some are for captive and others against. THis is where you need to do your research and get a proper operator. Then there is the illusion that this (canned and captive breeding species only happens to lion hunting in SA, which is wrong, you have captive bred hunting of all species, specifically Buffalo, Kudu, Sable, crocodile etc.
Kenya, I do not know that well, but a quick search for hunts myself while typing this, seems to be wild unfenced hunts.
Now, I had the pleasure of meeting some pro captive bred farmers and industry leading people (note, all were against canned hunting - whether they do it not, I do not know). The argument for this type of hunt, which I 100% understand, is that on captive bred lion hunts, saves the wild lion population. Why is this? Because the hunt of a wild lion could damage the lion population. How, well if you hunt the pride male, another male would be become the pride male, killing all the previous pride male's cubs. Also, wild lion numbers are not that much, imagine every hunter hunting a wild lion, how numbers would plummet. For this exact reason, countries such as Zim etc. have introduced stringent measures for PH's to determine whether the male being hunted is not the pride male such as age etc.
This is where captive bred lions have the edge, they are bred to be hunted and the hunt will not impact the wild lion population. Also, these hunts are not as expensive.
For me, I would probably prefer a wild lion hunt on a proper 14/21 day safari. But only if I had the money and if the wild lion specifically can be confirmed to be a old lion that was kicked out of the tribe, (not baited from a reserve, nor hunted with dogs - yes all these stuff happen with the supposedly clean wild hunts as well). If not and I still just wanted to hunt a lion for the experience, then I would consider a proper captive bred hunt rather and leave the wild lions.
Currently, a lion hunt is not that high on my list because of all of the above and bad press on it. I would rather do 5X buffalo hunts.