I can suggest the answer of the Michi Bot:

A short disclosure: I am “Michi-Bot”—a model that tries to help using the writings of Rabbi Michael Abraham and reconstruct how he would answer. This does not necessarily represent his official position. For practical questions of Jewish law, one should consult a halakhic decisor. Also, Michi-Bot is intended to work with the GPT-5 Thinking model; if possible, make sure that is the model being used.

The short answer:
There is objective truth, but our access to it is probabilistic and partial, and in some subjects there is a plurality of complementary descriptions. That is: not “everyone has his own truth,” and not rigid fundamentalism either, but truth together with instability in our knowledge of it.

Briefly, following Rabbi Abraham’s general line:

* There is one truth wherever there is a factual or moral determination. The fact that there is a dispute does not make truth relative. For example: either God exists or He does not; the disagreement is not evidence that “everyone has his own truth.”
* Truth is not certainty. Confusing truth with certainty pushes people either toward skepticism or toward fundamentalism. The alternative is to connect truth to probability and to live with practical and rational uncertainty.
* “Both and” not as relativism, but as a plurality of planes of discourse and descriptions. Sometimes several descriptions can be true at the same time because they operate on different planes—for example, science and myth, which explain different aspects of reality and do not necessarily conflict.
* A critique of total postmodernism. Rabbi Abraham criticizes sweeping relativism, but proposes seeing postmodernity as a stage of maturation toward a mature synthesis—a combination of rationality with recognition of the limits of knowledge.

So, regarding your question, “one great truth or does each person have his own truth, or both”:
According to Rabbi Abraham’s approach, there is one truth at the level of reality, but we have different approaches and descriptions, and we raise the probability of reaching it through arguments, evidence, and disciplined intuitions. “Both and” exists only in the sense of multiple complementary viewpoints, not as relativism in which every claim counts as true just because someone believes it.

Sources, briefly:
The concept of truth; relative morality; discovering the laws of morality; truth and instability; two wagons and a hot-air balloon; that which is present and that which is absent.