The main focus of this question is on "understanding reality", which is the domain of science. So, the first question is whether Buddhist insight meditation practice even qualifies as a science (i.e. a means of understanding reality).
Science (from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. In an older and closely related meaning, "science" also refers to a body of knowledge itself, of the type that can be rationally explained and reliably applied.
So, the criteria for calling something science (at least by Wikipedia standards) are:
- it is systematic
- it builds and organizes knowledge
- it relies on testable explanations and predictions as a basis for knowledge
- it takes the universe as its frame of reference
- it can be rationally explained and reliably applied
Buddhist insight practice fits all of these criteria; insight meditation is entirely systematic, it builds and organizes knowledge (more on knowledge later), its explanations and predictions are testable, it takes the universe (from a phenomenological POV) as its frame of reference, and it can be rationally explained and reliably applied.
So, Buddhist insight practice can at least be considered scientific.
Rather than focus on "which is better" (and get close-voted again), maybe we can agree to compare the two systems of "investigation into the nature of reality" objectively:
Buddhist insight takes as its paradigm a form of phenomenology or phenomenography, wherein:
there is only one world, one that is ours, and one that people experience in many different ways
It is therefore understood to be a means of understanding the nature of so-called "subjective" reality, i.e. one's own realm of phenomenological experience.
The modern scientific method, on the other hand, generally takes a stance of philosophical materialism, wherein:
matter is the fundamental substance in nature, and that all emergent phenomena (including consciousness) are the result of material interactions.
It is therefore understood to be a means of understanding the nature of impersonal material qualities from an "objective" (i.e. impersonal) point of view.
Here's where the controversy arises, so hopefully we can avoid it to some extent by comparing the individual claims of reliability (somewhat) objectively and leaving the reader up to their own conclusions.
Material science relies upon quantity and quality of empirical data that is independent of an individual frame of reference (i.e. it must be reproducible in all circumstances, not affected by experimenter or subject bias). The certainty of its claims are therefore dependent on the perceived likelihood of the objectivity of the data supporting them. For all intents and purposes, this provides a fairly good understanding of the nature of reality; the ability to build upon and modify prior understanding has allowed for incredible breakthroughs in our ability to interact with the material world.
The potential downside to this reliance on impersonal data is that it can and often has led to dogmatic refusal to accept new methodology or even evidence (e.g. Einstein's refusal to accept quantum mechanics).
It also has as a limitation its own ability to perceive the universe as a whole (so far, for example, it can't). This sort of limitation is what Rupert Sheldrake gets at in his discussion of scientific dogmas. He lists ten dogmas currently held by the modern scientific community that may very well turn out to be false:
- That nature is mechanical.
- That matter is unconscious.
- The laws of nature are fixed.
- The totally amount of matter and energy are always the same.
- That nature is purposeless.
- Biological inheritance is material.
- That memories are stored as material traces.
- The mind is in the brain.
- Telepathy and other psychic phenomena are illusory.
- Mechanistic medicine is the only kind that really works.
The point here is that the modern scientific method has led us to many of these dogmas through its locality - i.e. it can't say anything about the universe as a whole, except by inference, which may and often is proven wrong as new evidence is found.
A third point is that the modern scientific method tends to confuse data with truth and thus discard data that doesn't fit with a theory as statistical errors, etc. This is very well-documented (if somewhat outdatedly so) in The Book of the Damned, written in 1919. The author points out quite well the difference between what is commonly held as scientific knowledge and what is absolutely true, saying:
It is our expression that the flux between that which isn't and that which won't be, or the state that is commonly and absurdly called "existence," is a rhythm of heavens and hells: that the damned won't stay damned; that salvation only precedes perdition. The inference is that some day our accursed tatterdemalions will be sleek angels. Then the sub-inference is that some later day, back they'll go whence they came.
By damned, he means facts that have been ignored because they don't fit with contemporary scientific theory.
Again, practically speaking, the potential non-universality of modern scientific knowledge is inconsequential; for all practical purposes, it works.
Buddhist insight knowledge, on the other hand, is in a sense terribly "impractical", since it can only ever be "known" by the individual. As the Buddha said, the dhamma is "paccattaṃ veditabbo viññūhi" - to be realized by the wise for themselves.
It is also obviously unable to say anything about impersonal phenomena, since such entities are outside of its realm of observation and thus considered mental concepts.
On the other hand, it claims to provide a certainty of knowledge that material science does not (material scientists consider such certainty meaningless, since their frame of reference is impersonal). For example:
When endowed with five qualities, monks, in no long time a monk penetrates and intuits the Unshakeable. Which five? Here, monks, a monk is one who has attained discrimination of meanings, is one who has attained discrimination of principles, is one who as attained discrimination of language, is one who has attained discrimination of the illuminating qualities (of knowledge), and he reflects upon the mind as liberated. When endowed with these five qualities, monks, a monk in no long time penetrates and intuits the Unshakeable.
AN. 5.95 Akuppa Sutta
So, from a Buddhist point of view, insight meditation is preferable in the sense that it is not subject to alteration. The reason for this is it is also considered to be universal (from a point of view of one's own experience) - i.e., it is understood to be applicable to all entities in the universe (one's own universe of experience).
As someone pointed out in the earlier question, the two types of investigation are fairly non-competitive; material science focuses on material, Buddhist mental science focuses on the mind. The former is more useful for conventional purposes like curing disease and blowing stuff up. The latter is only useful for limited purposes like freeing oneself of all suffering.