INTP and ILI are both pretty much describe the same type of individual, but one attributes traits to Ti-Ne and the other to Ni-Te. For example, detachment is supposedly due to Ti in MBTI and Ni in Socionics. So the question isn't the types themselves, but rather the rationale behind what causes typology. Most notably, what attributes are due to what information elements?
My main beef with the MBTI is Ti as detachment. What of ISTP and ESTP? Se is both an emphasis on raw experience and living closely with reality. For Ti to be compatible with it, it must not impede on this way of life, but we can already see that Ti is the supposed source of INTP detachment. It cannot be Ne either, because an ENTP has a reputation for focusing on reality directly for the possibilities/implications it holds. Obviously we can't decide one way or another by one detail, but that's all I've found so far.
I think what needs to be further addressed is the nature of shadow functions in MBTI. I came from a model which suggests that we only use 4 elements and that these mix to make pseudo-function attitudes of the other 4. It seems that a great deal of the MBTI approach hinges on the role of the unconscious or conscious control. Here I can only speak from personal experience, and I find that nearly all of my thought processes that I'm not currently focusing on are 'unconscious', and that how much I can control something is purely related to how developed it is through my use of it. Furthermore, I've had both 'Thinking' and 'Feeling' functions go out of control and have found it necessary to repress them.
Note that there are two main versions of the MBTI. Some people refer to MBTI as the four dichotomies, which makes for something akin to the big 5. Others use a psuedo-Jungian approach, taking the MBTI type descriptions and extrapolating back towards the Jungian functions. This is distinct from the actual followers of Jung, as most notable in the differences of interpretation of the introverted functions.
Also note that I have since cropped this to be much shorter.