Here is some of what Master Sheng Yen says on sudden enlightenment and also some specific points on Linji. Sheng Yen is a modern Chan Master with transmission in both the Linji and Caodong lineages.
Firstly from Hoofprint of the Ox by Master Sheng Yen and Dan Stevenson, beginning of chapter 3, p107-108:
On the thematic perspective, he gives the example, following the Heart Sutra, that "form is already emptiness, emptiness already form"; if we can go directly to this view, there is no need to first reject form, then emptiness, etc. in sequence. (p108). Similarly there is no need for the sequence of the standard Mahayana bodhisattva path if we can immediately "identify with the innate Buddha-nature and manifest the enlightened mind all at once" (p109).The distinction between sudden and gradual representations of the Buddhist path may be considered from several perspectives [...] From the standpoint of temporal process, sudden refers to what is completed instantaneously, all at once. Gradual implies a time gradient or a step-by-step ascent over time. From a spatial or dimensional perspective, one could say that in the sudden approach there is no motion from "here" to "there"; no shift in position or movement from one realm to another takes place, whether it be from samsara to nirvana, delusion to enlightenment, or so on. In fact the metaphor of spatial delimitation collapses altogether with the sudden perspective, for "here" is "there", and "there" is "here". The gradual approach, on the other hand, not only sets up spatial distinctions, but represents progress toward enlightenment as a dialectical displacement from one perspective or realm to another -- for example , from existence to emptiness, from emptiness back to existence, to both, to neither.
Finally, there is the thematic or dialectical perspective. [...] The gradual approach entails a sequence of distinct thematic positions that build on one another or displace one another in a dialectical fashion, until the final true vision of highest enlightenment, or emptiness, is revealed. [...]
In the case of the sudden approach, the full and unalloyed vision of perfect enlightenment is presented all-at-once and is apprehended all-at-once, without resort to dialectical shift or temporal development. No conveyance from one mode to another takes place; no process of thematic manipulation or shift in conceptual perspectives is necessary -- just an immediate expansion of horizons.
However, he feels that whether this is possible depends on a person's aptitude (p109):
This follows what Hui Neng is indicated to have said (possibly ahistorically) in chapter 8 of the Ming version of the Platform Sutra. It also explains why Hui Neng is said to have become enlightened just from hearing a phrase from the Diamond Sutra even though this doesn't seem to work for the rest of us.If one possesses keen karmic roots and one's mind is already quite pure due to extensive practice in past lives, then in one's present life one may be properly disposed to grasp and make effective use of the sudden teaching.
Someone in class mentioned the possibility that sudden enlightenment means that people are either fated to become enlightened or not, which I assume refers to this last point. But the idea as I understand isn't that one method is fundamentally better, just that there is no need for gradual process for anyone who is able to skip it. It could definitely been seen as elitist, but it seems hard to deny that different people do have different aptitudes, if nothing else because not everyone will have the opportunity to hear the appropriate teachings or find an appropriate teacher at the appropriate time. This sort of idea isn't unique to the concept of sudden enlightenment, because in earlier Buddhism a common assumption is that one must be a monk to be enlightened, but not everyone will have appropriate conditions to become a monk in their current life.
For more on sudden enlightenment, see also the rest of this section of Hoofprint of the Ox and section 4.12 in Sheng Yen's Orthodox Chinese Buddhism.
Moving on to Linji's specific teaching methods, still in Hoofprint of the Ox, first section of chapter 7, p120:
And as for the overall strategy of hitting and shouting instead of answering questions (same section, p120-121):[Shouting and beating] are simply intended to help those with incorrect focus or insufficient energy to find the proper integrity and determination necessary to practice effectively. The master helps the student tune the mind and spirit, but the student is the one who intimately brings the training to its conclusion. In a sense, it is like a chick hatching from an egg. While the chick struggles and presses from the inside, the mother hen pecks on the shell from the outside. By doing so at the appropriate time and in the appropriate way, the hen helps the chick hatch that much easier.
See also the description of Sheng Yen's own experiences with Masters Lingyuan (p6) and Dongchu and (p7-9) in Hoofprint of the Ox.Some masters used to refrain from answering any queries that the student had about these episodes. Instead, they might beat or verbally abuse the person without any explanation. [After this the student] would certainly remain unsettled. Should the student eventually return to question or, perhaps, respond the master, he or she might once again be beaten, thereby leaving him or her even more deeply puzzled.
At this juncture one's [the student's] whole being might be directed toward understanding the reason for this treatment, to the point where one's consternation about the master's actions even supersede the original question. This sort of thing could well go on for years, ultimately leaving the student in utter confusion, with absolutely nothing sure on which to hold. Should one then decide to leave the monastery and try another master, one may well find oneself confronted with further beatings and no answers. However, after years of having the rug constantly pulled out from underneath you like this, in the end you may truly become an ordinary person with nothing to do. In fact, this was precisely Linji's own experience.