I nearly always play a healer on MMOs so when I was looking into FFXIV and asking friends the difference between sch and whm, they were saying sch was better because they had shields, a fairy to help heal, a really op single target "oh crap" button you could use up to 3 times per minute (back then lustrate was a flat 25% hp recovery, even in cleric stance), and if you were good enough, you could put out some decent dps on top of everything else.
It worked out for me because I'm a big fan of classes that use books as their weapons, and in many mmos those are usually reserved for the dark sorcerer/necromancer types. Summoners fit that role since they're like poison mages here, but I was very pleased to know you could be a healer and still have a book.
I leveled whm later though, and while sch was still my preference, I no longer believed one was better than the other in every situation, and ideally you wanted both in full parties.
I sort of like ast, but I am not a fan of RNG. I pretty much only play it for funsies in expert roulette or 24 man raids if I am going with a friend, so I can give them all the cards.