There is no Biblical obligation to tell the story of the Exodus on Pesach night. The verses which seem to obligate one are understood to refer to either cognitive actions, other days of the year, or parts of other obligations .
Shemot 13:3 – "זָכוֹר אֶת הַיּוֹם הַזֶּה" – This approach might dismiss this verse as a source for the obligation on several grounds:
זכירה בלב – The verse uses the verb "זָכוֹר" rather than "אמור" (or the like) and thus might refer to remembering in the heart and not recounting via speech.
Heading – It is also possible that the phrase should be understood as a heading for what follows rather than an independent obligation. The nation is told to "commemorate the day you left Egypt" and the rest of the unit then explains how to do so: don't eat leavened bread, do the Pesach service, and celebrate Chag haMatzot for seven days.
Obligation for the rest of the year – In addition, it is not clear if the verse refers to remembering specifically on Pesach or throughout the year. See Mekhilta DeRabbi Yishmael13:313:14About Mekhilta DeRabbi Yishmael Shemot who reads this phrase as being the source for remembering the Exodus daily.2
Devarim 16:3 – "לְמַעַן תִּזְכֹּר אֶת יוֹם צֵאתְךָ מֵאֶרֶץ מִצְרַיִם כֹּל יְמֵי חַיֶּיךָ" – These sources would likely reject this verse as a source since the word "לְמַעַן" suggests that the remembering mentioned in the verse is not a commandment in and of itself, but simply the purpose of the obligation to eat matzah mentioned earlier. In addition, the verse speaks of remembering rather than telling, and specifies that this commemoration should take place "כֹּל יְמֵי חַיֶּיךָ" rather than on Pesach night specifically.3
Shemot 12:27 / 13:8 – "וַאֲמַרְתֶּם זֶבַח פֶּסַח הוּא"/ "וְהִגַּדְתָּ לְבִנְךָ... לֵאמֹר" – These verses explicitly mention speech4 and clearly refer to Pesach night. However, as they both speak of the recounting as accompanying the eating of the Pesach sacrifice, these sources might suggest that the telling is subsumed under the larger mitzvah of eating, and therefore does not constitute its own obligation. Alternatively, the recounting is simply the purpose of the eating and therefore is a קיום המצוה but not an independent obligation.
Shemot 13:13 – "וְאָמַרְתָּ אֵלָיו בְּחֹזֶק יָד הוֹצִיאָנוּ" – Though this verse directs one to verbally speak about leaving Egypt, its context is not Pesach, but the redemption of the first born. Thus the verse only directs one to tell the story if a child asks about the ceremony but says nothing about any obligation on Pesach night.
Devarim 6:21 – "וְאָמַרְתָּ לְבִנְךָ עֲבָדִים הָיִינוּ" – The context of this command is also unrelated to Pesach. It speaks, instead, of a general obligation to explain to one's children that the reason to keep Hashem's commandments is the fact that He freed the Israelites from slavery in Egypt.
Cognitive /active/ verbal
"כל המספר"" versus "כל המרבה לספר" – In Seder R. Amram Gaon, the text of the haggadah reads, "וְכָל המספר בִּיצִיאַת מִצְרַיִם הֲרֵי זֶה מְשֻׁבָּח ", instead of "וְכָל הַמַרְבֶּה לְסַפֵּר". This might support the idea that many Geonim did not count the telling of the story as a Biblical commandment. The very act of telling the story (not the elaboration upon it) is praised because it was not obvious that everyone would do so.
No blessing on haggadah – This position would explain there is no blessing over the telling of the story in the haggaddah because there is no Biblical obligation to do so.
Story of the Five Sages
Telling Through Eating
The obligation to tell the story of the Exodus does not necessitate a verbal retelling, but is rather fulfilled through the act of eating the Pesach sacrifice. By eating the lamb with matzah and maror, one re-enacts the original Pesach thereby effectively recounting the essence of the story.
Source for the mitzvah – According to this approach, the verses in Shemot 12:26-27, Shemot 13:3-8 and Devarim 16:1-3 which speak of remembering the Exodus as one offers the Pesach teach that the mitzvah is action-oriented and the recounting takes place through the act of eating itself. The language of "וַאֲמַרְתֶּם זֶבַח פֶּסַח הוּא לַי"י" or "וְהִגַּדְתָּ.... לֵאמֹר" is not understood literally to refer to verbal expression, but to the conveying of information.
Comparison to other mitzvot – The Rosh compares the obligation to remember the Exodus when eating the Pesach to other mitzvot which similarly commemorate the enslavement and redemption, such as redemption of firstborns or celebration of Shabbat and holidays. In each case one need not actively speak about the Exodus; the fulfillment of the mitzvah itself serves to commemorate it.
No blessing on haggadah – The Rosh explains that there is no blessing made over telling the story in the haggadah, just as there is no blessing over commemorating the Exodus when redeeming a firstborn. In both cases, the blessing is instead made over the active part of the mitzvah (eating of matzah and maror, redeeming of the son, etc.) which itself constitutes fulfillment of the commemoration.
"כל המספר"" versus "כל המרבה לספר"
Focus of the commandment – According to the Rosh, the night is experiential in nature.
Rejection of other potential sources – The verses in Shemot 13:14 and Devarim 6:20-21 make no reference to the Pesach offering and thus cannot be understood as a command to recount the story through eating. However, they also do not obligate any retelling on Pesach at all, referring instead to speaking of the Exodus during other occasions during the year (when redeeming a first born and when teaching children about the import of Hashem's mitvot.) As such, they can not be brought as a source to obligate a verbal telling of the story on the eve of the 15th..
Verbal Recounting
There is a Biblical obligation to verbally tell the story. This position subdivides regarding whether the obligation exists only if a child questions or even if not:
Only If Child Asks
The obligation only entails responding to a child who asks. Had there been no child, a parent would not have to recount the story.
Source for the obligation – As the only verses which clearly speak of verbally retelling the story of the Exodus specifically on the eve of the 15th (Shemot 12:27 and 13:8 ) , do so only in the context of responding to a child, this position limits the obligation to such a scenario.
Purpose of commandment – The purpose of the commandment would seem to be to ensure the continuation of the tradition. See Ramban
Source for the obligation – Rambam looks to two verses, Shemot 13:3 ("זָכוֹר אֶת הַיּוֹם") and 13:8 ("וְהִגַּדְתָּ לְבִנְךָ"), which when combined, teach that there is an obligation to verbally retell the story, even when no child asks. The two verses complement each other, each compensating for what the other lacks. While Shemot 13:8 refers to a verbal retelling which takes place on the eve of the 15th, it limits the obligation to responding to a child. Shemot 13:3, on the other hand speaks only of remembering and is unclear as to the timing of the commandment, but expands the obligation to all.
"זָכוֹר אֶת הַיּוֹם הַזֶּה" – Rambam maintains that the word "זָכוֹר" refers to speech rather than to memory by comparing it to the command " זָכוֹר אֶת יוֹם הַשַּׁבָּת", which is also understood to refer to a verbal action, the recitation of kiddush.
Focus of the evening – According to the Rambam, the focus of the evening is not the experience of eating, but speaking and learning. This matches Rambam's general approach to mitzvot where he favors use of the intellect in one's service of Hashem and fulfillment of obligations.
Influence of the Destruction of the Mikdash – It is possible that after the destruction of the Mikdash, when there was no longer a Pesach offering, there was a need to change the focus of the evening from the previous emphasis on the sacrifice and meal to the story itself. This is comparable to the general shift from sacrifice to prayer.
"כל המספר"" versus "כל המאריך לספר" – Since the Rambam maintains that there is an obligation to tell the story, it would be odd to praise someone for simply fulfilling a Biblical obligation. Thus, it is logical that he prefers the version of the haggadah that praises one for expounding at length about the story (וְכָל הַמַּאֲרִיךְ לְסַפֵּר בִּיצִיאַת מִצְרַיִם הֲרֵי זֶה מְשֻׁבָּח).