i gave a lecture regarding this over Shavu'oth, let me see if i can sum my talk for you.
The Torah is a copy of everything that was said, so one might think it's redundant to then have the Luchoth there as well, but they are two entirely different things. The Sefer Torah is the words of everything, whereas the Luchoth are the sign of contract while also being the contract. Which is why they are called "לוחות הברית" - the tablets of the covenant/contract." So their function has two purposes, one of which being to have written the terms of the agreement, the second of which is to by a physical symbol of the agreement, as is the case with the other covenants in the Torah (which is the same as how covenants were made in the Ancient Middle East).
Genesis 31:46-48
וַיֹּאמֶר יַעֲקֹב לְאֶחָיו לִקְטוּ אֲבָנִים, וַיִּקְחוּ אֲבָנִים
וַיַּעֲשׂוּ-גָל; וַיֹּאכְלוּ שָׁם, עַל-הַגָּל.
And Jacob said unto his brethren: 'Gather stones'; and they took
stones, and made a heap. And they did eat there by the heap.
וַיִּקְרָא-לוֹ לָבָן, יְגַר שָׂהֲדוּתָא; וְיַעֲקֹב, קָרָא לוֹ
גַּלְעֵד.
And Laban called it Jegar-sahadutha; but Jacob called it Galeed.
וַיֹּאמֶר לָבָן, הַגַּל הַזֶּה עֵד בֵּינִי וּבֵינְךָ הַיּוֹם; עַל-כֵּן
קָרָא-שְׁמוֹ, גַּלְעֵד.
And Laban said: 'This heap is witness between me and thee this day.'
Therefore was the name of it called Galeed;
The sign of covenant is supposed to not be owned by any one of the parties, but be accessible to all. Which is why Jacob and Laban build the stone pile in an area that belongs to neither party. And why it is not an accident that God makes the Rainbow as the sign of the covenant to not flood the Earth again. He makes a sign that is not owned by any of the three parties of the covenant, while being accessible to all three. The first party is God, which is why the Rainbow is in the heavens, but is still visible on Earth. The second is mankind (Noah and his family) who have control of the Earth but can see the heavens. And the third is the animals, who needed a sign that they could see, without the risk that it could be taken over by mankind on Earth. Hence, the Rainbow.
Genesis 9:12
וַיֹּאמֶר אֱלֹהִים, זֹאת אוֹת-הַבְּרִית אֲשֶׁר-אֲנִי נֹתֵן בֵּינִי
וּבֵינֵיכֶם, וּבֵין כָּל-נֶפֶשׁ חַיָּה, אֲשֶׁר אִתְּכֶם--לְדֹרֹת,
עוֹלָם.
And God said: 'This is the token of the covenant which I make between
Me and you and every living creature that is with you, for perpetual
generations:
Which is why according to some of the sages, the Ten Commandments were not split up as 5 on one tablet and 5 on the other, as this does not make contractual/covenental sense. It makes more sense for each tablet to be one complete copy of the ten, and then two tablets for the 2 parties, God and the nation of Israel.
Midrash Rabbah on Exodus 37.6
עשרת הדברות כיצד? היו עשויין ה' על לוח זה וה' על לוח זה כדברי ר'
יהודה. ור' נחמיה אומר: י' על לוח זה וי' על לוח זה, שנאמר שמות לד
The Ten Commandments, how were they done? There was made 5 upon this
tablet and 5 upon the other tablet according to the words of Rabbi
Yehudah. And Rabbi Nehemiah says: Upon this tablet there is 10 and
upon the other tablet is (the same) 10, as it is written [in Exodus
34].
For more information on this topic, and an answer as to why then both copies would be placed in the Ark, please read this article by Dr. Meshulam Margaliot (Emeritus, Dept. of Bible Bar Ilan University)
What was Written on the Two Tablets?
…we are dealing with the text of a covenant, a type of contract
between two (or more) parties. For obvious reasons, it is customary
for every written contract or agreement to be issued in duplicate,
each party receiving a complete copy of the agreement, contract, or
covenant. This was also the practice in the ancient Near East. The
most famous example of two copies of a diplomatic agreement between
two kingdoms is the treaty containing the pact made between the
Egyptian Pharaoh Ramses II and the Hittite King Hattusilis III, c.
1270 B.C.E. The Egyptian copy was found in Egypt, and the Hittite one
in the capital of the Hittites, in eastern Turkey. The contents of
both copies are identical. It would be reasonable for the pact made at
Sinai to be issued in two copies, one for the Lord, and one for the
Israelites. This practice explains why one tablet did not suffice,
rather two were needed. It is self-evident that the Lord's tablet had
to be placed where the Divine Presence (shechina, Biblical Hebrew
kavod) was found (see Ex. 29:43 and 40:34), in the Holy Ark made
specifically for this purpose: "And deposit in the Ark the Pact which
I will give you" (Ex. 25:16), "He took the Pact and placed it in the
ark" (Ex. 40:20). "The Pact" [edut] is used as shorthand for the "two
Tablets of the Pact" (Ex. 31:18), also called shnei luchot habberit,
the "two Tablets of the Covenant" (Deut. 9:15). But what about the
Israelite's copy, on the second Tablet, where was that copy placed?
Here we note a common practice in the ancient Near East. When a treaty
was made between parties of unequal status, the lesser partner, or
vassal, would place his copy of the pact in the temple of his god, the
reason being that the vassal had then to take an oath in the name of
his god, to "the great king." Depositing a copy in the temple of the
vassal strengthened the vassal's obligation to the greater king. In
addition, sanctity was ascribed to the treaty itself, because the gods
of each side were witness to the agreement: Compare Laban's words to
Jacob after striking a treaty: "May the G-d of Abraham and the god of
Nahor" --their ancestral deities-- "judge between us." (Gen.31:53)
Since the Israelites had the status of vassal vis-à-vis G-d and were
the lesser partners to the Covenant, it was reasonable for them to
file their copy of the Pact in the Holy Ark of the Lord their G-d.
Thus we conclude that both Tablets were placed together in the Ark in
the Tabernacle…
Source: http://www.biu.ac.il/JH/Parasha/eng/kitisa/mar.html
