I see two separate issues.
(1) transferability of skills can be asymmetric
It can, for example, be easier to go from Violin to Viola than from Viola to Violin, (and perhaps snooker to American pool, over American pool to snooker) without violin being a harder or somehow more impressive instrument than Viola. It's more about whether the instrument/game specific sub skills happen to be amongst the slowly acquired sub skills.
(2) which, between snooker and pool, is deeper and more developed?
Snooker is often cited here. But I think we should be more circumspect.
But before I justify that, let me introduce a depth-of-development concept for a sport or skill. No matter the skill or sport, we have the notions of "best in the world," and "greatest of all time." What makes a skill look impressive to us is usually not something absolute; it is that someone does it better than almost anyone else in the available talent pool.
If you were to gather the world's 50 best unicyclists into Wembley Stadium and have them demonstrate their skill, they would seem unbelievably talented and skilled and their display would be unprecedented.
If you were to gather the world's 50 best at soccer-ball control into Wembley Stadium and have them demonstrate their skill, they too would seem unbelievably talented and skilled and their display would be unprecedented.
But there is a key difference.
The soccer skill is far more deeply developed in the population. There are billions of preadolescents whose heroes are soccer players, who see soccer skills as highly valued in their communities and a key to the future they yearn for. As a result, there is a large meritocratic funneling such that the world's 50 best comprise a far more impressive group in an absolute sense. Importantly, we don't see this depth when we're looking at the best because we often mistake rarity for depth. Those impressive unicyclists probably wouldn't be the best in their local county if unicycling had a generation with world-wide soccer-like popularity and culling.
The best surfers in the world look amazing. But the talent really comes just from people who happen to grow up around certain coastal communities. Half of the best hockey players in the world come from Canada or Sweden (just over 50 million people). Surfing and hockey are less developed sports than soccer--and less developed even than American football or baseball or basketball.
Snooker has a genuinely global fan and federation footprint (governing bodies, TV viewers, players), but the world-class player pipeline is still much less geographically distributed than that footprint suggests. A very large share of top snooker players are either from the UK or from China and living/training in the UK. If we ask what fraction of the prize money goes to people who can eat breakfast at home and then walk, drive, or hop a train to Sheffield by lunchtime, I suspect the answer is: quite a lot.
Right now, 10 of snooker's top 16 were from the British Isles: England, Wales, Scotland, or Northern Ireland. And several of the non-British names that make the list look more international--Zhao, Si, Ding, and likely others--are in fact living or training in Sheffield and the UK snooker system. So while snooker is clearly international in one sense, its elite talent-production base is still surprisingly concentrated.
That does not prove pool is deeper. But it should at least make us hesitate before casually assuming that snooker’s stronger institutional structure means it must have the more developed talent pool. My own guess is that, while pool is still an undeveloped sport by major-sport standards, it has become the more globally developed of the two. The top end is no longer mainly American. The top 16 active Fargo players come from Vietnam, Austria, Poland, Scotland, Singapore, the Philippines, Iraq, Spain, Taiwan, and USA. The elite is more geographically distributed than it used to be.
So even though pool’s governing structure is a mess, its talent base may actually now be broader and deeper than snooker’s. If that’s right, the goal is not to imitate snooker mechanically. It’s to avoid squandering the broader global player base pool has managed to create.
Snooker may have settled into a kind of local maximum: a very successful UK-centered sports/entertainment product that is international enough to look global, but still concentrated enough to make outside breakthrough unusually hard.