As always it depends on what you are wanting - bigness, "smallness", wildness, history, water-created features, a "theme park" experience, crowds, solitude etc etc?? In Europe at least many caves are operated as commercial ventures and, as a result, are less likely to be nominated as WHS unless they happen to be part of a bigger site inscribed for more general reasons. If Causses et Cevennes gets inscribed this year I will be interested to see if it includes Aven Armand which is inside the Cevennes National Park - I found it to be one of the most spectacular I have seen for its stalagmites etc.
Another "problem" with visiting caves is that, because they are potentially "dangerous" for visitors, then, particularly in "developed countries", the visit experience can turn into a rather "organised" one!
Mammoth Cave is, as the name suggests, well ....very big! But beyond that I wouldn't rate it that highly. You get the full "Mr Ranger Sir" experience on a guided tour which is highly organised with computerised bookings. The walk from the far corners of the car park could be as long as the walk underground! There are a number of different tours to choose from - and the descriptions at the site should allow you to choose the most appropriate for your interests/capabilities. However some (including the one you want!) might be fully booked at the time/day you want to go. Certainly if you were in the area you should take it in but I wouldn't make a massive detour for it (unless you "need" to tick off a WHS!).
Of the Caves of the Aggtelek and Slovakian Karst I have only visited Dobšinská. This was of interest to me primarily for its Ice Pillar and I have been criticized on this site for not reviewing it highly enough. If I had to choose I would go to Aven Armand in preference – but there are over 700 caves in the system!
In Slovenia I have only visited Postojna and, unfortunately that country later chose to inscribe, what the review on this site, calls the nearby but "less famous" Skocjan caves. Postojna has the full "entry on a train" if you want that sort of thing but will be far more crowded now even than when we visited. It was very impressive but the reviews of Skocjan seem to indicate that it might provide a less sanitised experience.
Malaysia (Borneo) has some fine caves and we visited Nias which is famous for its Bats, Swifts, the poles for collecting the "Birds nest soup nests" and the remains of early man. We really enjoyed it and had it entirely to ourselves in the evening gloom as the bats and swifts wheeled in and out with the jungle beyond. Unfortunately Malaysia gave me another "near miss" by choosing Gunung Mulu for inscription in 2000. It is more remote of access (Nias is situated naturally on the route along the N Borneo coast from Kuchung up to Brunei and Kota). Again, from the review on this site, I really regret not having visited it with its overnight stay, jungle walks etc – it also has the swifts and bats. If ever I went back to Borneo I would certainly try to take it in.
But for a proper "caving experience" you shouldn't look to the famous and over-touristy WHS examples – instead contact your local caving club for a beginners "initiation" trip and experience a "real cave visit" crawling through narrow squeezes etc and getting completely soaked!