[Gordis]

There must be two approaches to torture in Mordor, I think.

I. One is physical and mental torture of living Men/Orcs. As refined, cruel and prolonged as it may be, it is by no means otherworldly and its time is necessarily limited (at least by the natural life-span of the prisoner). It takes a lot of art to keep the tortured prisoner alive, but once the tortured body can endure no longer and dies, the spirit is released and go to Mandos - and the prisoner is free, so to say. Not even Sauron can keep a houseless Men's fea from receiving the Gift.

It seems it is this kind of torture that mostly goes on in Barad-Dur, both for Men and for Orcs (Black Pits):

The Black Pits take that filthy rebel Gorbag!’ Shagrat’s voice trailed off into a string of foul names and curses. `I gave him better than I got, but he knifed me, the dung, before I throttled him. You must go, or I’ll eat you. News must get through to Lugbúrz, or we’ll both be for the Black Pits. Yes, you too. You won’t escape by skulking here.’

It seems it is this kind of torture MOS refers to speaking of Frodo:

And now he shall endure the slow torment of years, as long and slow as our arts in the Great Tower can contrive, and never be released, unless maybe when he is changed and broken, so that he may come to you, and you shall see what you have done.

I think, MOS, being a living Man, albeit a sorcerer, simply has limitations. He hasn't got access into the Spirit World himself and cannot move others there. Physical and mental torture of living prisoners is all he and his minions are capable of. If he feels something worse than that is in order, MOS has to ask Sauron to do it personally or send the prisoner to the nazgul in Minas Morgul. In both cases it is somewhat like a loss of face and I doubt MOS does it often, and only in most important cases. Frodo, who was considered simply a captured spy with no connection with the Ring, probably was not considered important enough.

II. The other type of torture is definitely otherworldly. Sauron and his nazgul had discovered means to keep a Mannish fea in Middle-Earth for all eternity and do as they please with it. For that a Man has to be turned into an undead wraith. It can be done by Rings of Power (as with the nazgul), it can be done by a Morgul knife, likely it can be done by other Morgul methods inducing "living death." The Barrow-Wight's incantation comes to mind here - likely it attempted to plunge the bodies of the hobbits into death-like sleep while their spirits would be still bound to their hroar:

Cold be hand and heart and bone,
and cold be sleep under stone

Likely with Eowyn the Witch-King referred to some method other than the Morgul knife through the heart, because first he had to bear Eowyn away to the houses of Lamentation, where is seems the later transformation would take place: flesh devoured and shriveled mind will be left naked at the mercy of the Lidless Eye. Note that it certainly implied trapping her human fea in some way: so it couldn't have been simple death.

Such a fate (ETERNAL mental torture) was in store for Frodo, had he been captured on his way to Rivendell:

'They tried to pierce your heart with a Morgul-knife which remains in the wound. If they had succeeded, you would have become like they are, only weaker and under their command. You would have became a wraith under the dominion of the Dark Lord; and he would have tormented you for trying to keep his Ring, if any greater torment were possible than being robbed of it and seeing it on his hand.'

I guess his place would have been in the Houses of Lamentation, if not at the foot of Sauron's throne.

Now, unlike MOS, the nazgul definitely despised the first kind of torture, likely seeing it as a child's play, an easy way out. After all, cruel and cunning as he was, the Mouth was nothing but a child compared to the nazgul. It is psychologically understandable: things the undead Ringwraiths would find really scary should last for all eternity, not for pitiful decades. Thus they didn't hesitate to apply such a dreadful otherworldly punishment even to misbehaving orcs or random humans facing them on the battlefield.

By the way, I believe the Houses of Lamentations were in Minas Morgul, not in Barad Dur. I see it as a place where lesser wraiths suffered prolonged mental torture.
Bethberry commented that the "Houses of lamentation was a very poetic expression, not something I would have expected from Witchie." It is poetic indeed, but much in line with the whole aspect of Witchie's abode, the Valley of Wraiths around Minas Morgul. Everything there is totally unlike the coarse Mordor proper: statues, misty river, meadows of pale flowers etc… like a scary enchanted dream.