It's all about winning. It's all a competition between mitzvot to determine which is the most important, and thus which takes precedence over the others.
Last time we were working on Esther 9:28. We're squared away with interpreting the repetition of "medinah umdinah" (to make a distinction between walled and unwalled cities, or between Shushan and other "unwalled" cities, or whatever), and "ve'ir va'ir" (to include anything next to the walled city or seen with it). But what about "mishpachah umishpachah"? This comes to include the priestly and levitical families, who can take off work to hear megillah reading. Thus, in the first round of the tournament, the megillah takes precedence over avodah (ok, not really "work", but the Temple service that the priests are doing).
Rebbi's house (150 years after the destruction of the Temple) would skip talmud torah to go hear the megillah, based on transitivity: megillah beats avodah, and avodah beats talmud torah, ergo megillah beats talmud torah. (And yes, we can assume transitivity -- we don't have any rock-paper-scissors scenarios in this sugya, let alone rock-paper-scissors-couch.)
But wait a second, when did avodah beat talmud torah? That round never happened! In fact, if we examine some midrashim (from Sanhedrin and Eruvin) about Joshua, the fight comes out the other way! Check it out: In Joshua 5:13-15 (from the haftarah for the 1st day of Pesach; since the avodah vs. talmud torah showdown could have been staged pretty much anywhere, was this venue chosen intentionally because the redemption of Purim is tied to the redemption of Pesach?), Joshua has an encounter with a divine messenger.
The Gemara wonders what Joshua was doing talking to this stranger at night -- what if it had really been a demon? (And what evidence do we have that this episode happened at night anyway? Real question here. Is it discussed in Sanhedrin? Or are we just to infer from Jacob's wrestling match that all adversarial human-angel encounters happen at night?) No worries: this mysterious man identified himself as "captain of God's host". Ah, but what if he was lying? No, we have a tradition that they wouldn't use God's name in vain like that.
According to this midrash, a few lines of dialogue are missing from the story. After sar tzeva Adonai identifies himself, he rebukes Joshua: "Last night you guys neglected the afternoon tamid [this is avodah], and now you're neglecting talmud torah!" Joshua asks "Which one of these did you come about?" The response (which is actually in the text): "Now I have come", i.e. I'm here about the infraction now; I didn't come about the other one yesterday! As Rav Shmuel bar Onya points out, this means talmud torah beats avodah! Zing!
Postscript: Joshua changed his ways. We know this from a scribal error. In Joshua 8, we have two statements that were clearly supposed to say the same thing: 8:9 says "vayalen Yehoshua' balailah hahu b'toch ha'am" (that night, Joshua spent the night among the people), and 8:13 says "vayeilech Yehoshua' balailah hahu b'toch ha'eimek" (that night, Joshua went in the valley). JPS points out that some manuscripts have vayalen in both verses (including the one quoted in the Vilna Shas! and apparently R. Yochanan's version, see below), and that the Syriac version of 8:13 also translates ha'am, not ha'eimek. But the rabbis didn't know that latter fact, so they said "Valley? What valley?" Rabbi Yochanan says that it means that Joshua spent the night in the omek (depth) of halacha. He saw the error of his ways and went back to talmud torah.
So now it would appear that talmud torah and avodah are tied 1-1. Time for the sudden-death round! Except the Talmud doesn't actually like sudden-death rounds; it prefers the la kashya structure, where everyone is a winner. So talmud torah wins for the masses (like, oh I don't know, the entire people of Israel whom Joshua was leading), and avodah wins for individuals (like the house of Rebbi) -- NCAA Division III if you will.
That result is contested. Does avodah really win for individuals? Mishnah Mo'ed Katan 3:8 bans certain mourning practices on joyous holidays such as Purim, but then Rabbah bar Huna (over in Mo'ed Katan) makes an exception for the funeral of a talmid chacham [student of the wise]. If a talmid chacham's funeral overrides Purim (even in regard to individual practices), this means that talmud torah beats megillah, and therefore beats avodah (since megillah definitely beats avodah - that's where this whole mess started).
Wait just a minute there -- you just brought a ringer onto the field! That funeral was kevod torah (honor for the Torah), not talmud torah (study of Torah)!
So now the ranking (for individuals) seems to be kevod hatorah at the top, then megillah, then avodah, then talmud torah.
Rava now brings in a new player: meit mitzvah (burying someone who has no family to bury him/her). As in chess or Shufflepuck, this player has to start at the bottom and work its way up. Meit mitzvah vs. talmud torah: a baraita says you can skip talmud torah for funerals and weddings. Didn't even have to break a sweat.
Meit mitzvah vs. avodah: This requires some midrash halacha on Numbers 6:7 The nazir can't become tamei for any of his dead relatives. The "and" in the list of relatives indicates that it is an exhaustive list. Therefore, the nazir can (and must) become tamei for a meit mitzvah. This is extended to anyone who is on the way to offer a pesach or whatever, even though being tamei would postpone these plans. Meit mitzvah 1, avodah 0!
Meit mitzvah vs. megillah??? (Cue "NBA on NBC" music.) Is it megillah because of publicizing the miracle, or is it meit mitzvah because of kevod haberiot (human dignity)? The winner is.... meit mitzvah! Kevod haberiot is so powerful that it can even override a negative Torah commandment (so it can crush a positive rabbinic commandment).
And that's where the sugya ends.
At the end of the day, kevod torah and kevod haberiot are both undefeated. Perhaps at the end of days, we'll get to watch them square off in a mitzvah Super Bowl, and then we can feast on their flesh in a banquet for the righteous.
And that just gets us to the middle of 3b. I'll post about the rest of 3b and 4a later.
UPDATE: I wrote:
In Joshua 5:13-15 (from the haftarah for the 1st day of Pesach; since the avodah vs. talmud torah showdown could have been staged pretty much anywhere, was this venue chosen intentionally because the redemption of Purim is tied to the redemption of Pesach?), Joshua has an encounter with a divine messenger.
Also, the Mishnah's definition of a walled city is a city that was walled at the time of Joshua, so there's another reason why this episode fits here.