Notice the language of the Talmud. No specific area of halacha is mentioned, simply "The law follows us". Also notice that the two sides are Beit Shammai and Beit Hillel.
The Talmud in Shabbos outlines Between 3 and 5 disputes between Hillel and Shammai themselves, a mere handful. However, throughout the mishnah, one can see many more argumens between Beit Shammai and Beit Hillel, the two sages' respective schools, which survived them. The wikipedia article on them counts 316, just in the Talmud! In fact, The Talmud in Sotah reprimands the two schools For insufficiently learning from their rabbis, saying that because of this disagreement increased, and the Torah became like 2 different entities. It was seemingly in this climate that the events related in Eruvin transpired. Up until this point, there simply hadn't been much dispute over the law. Suddenly, hundreds of disagreements were sprouting up left and right. I'm afraid an outline of the specific arguments is beyond me, but the 8th chapter in Brachot, or the 1st chapter of Yebamoth mishnah 4, come to mind, for starters.
To complicate things further, Etz Joseph brings a rule from the beginning of Avoda Zara that when Tanaaim argue, we generally follow wisdom and number, siding with the wiser majority. In this case, both parties had one advantage. Beit Hillel had the majority, but Beit Shammai had more brilliant minds. Given the stated rule in the Talmud, perhaps we can add that they argued for so long because they weren't sure how to deliberate in such an uncommon case, until given Divine input1. So we can add to the pile a need to clarify just how to deliberate given the rare, perhaps unprecedented stale mate with which they were faced. Tosafot alludes to this as well.
Furthermore, Ritvah brings a quandary from the French scholars about the concept of 'these and these'. How can two contradictory rulings be true. They answer that Moses had both rulings explained to him when he went up to get the Torah. When he asked about definitive ruling, God told him that it would be left to the Sages of each generation to decide upon. So we see that Beit Shammai and Beit Hillel were both right. They both had sound, irrefutable, and divinely ordained positions. Before the message of 'these and these' though, they assumed, as any rational mind would, that in the case of objective law, there is one right answer! So the three years was likely also spent in a hopeless gridlock, where both sides tried and failed again and again to find a flaw in each other's rulings2.
- They had much disputed halachic material to cover, upwards of a hundred times what their predecessors were faced with, much of which may have surfaced along the way.
- They had to figure out how to rule with equal halachic priority
- They were attempting and reconcile the assumption of one right approach with the persisting existence of two.
1. The Talmud does provide a recourse if neither part has wisdom and number; follow the stricter opinion for biblical and the more lenient opinion for rabbinic. Etz Joseph doesn't mention that though, and indeed the Talmud in eruvin does not follow that deliberation, or the law would follow Beit Shammai, who with few exceptions take a more strict approach than its contemporary school. The implication of the whole story in Eruvin is that Beit Hillel and Beit Shammai where sure that there was only one 'right' way. They had to be told that there can be more than one correct ruling. It appears evident that this was a later addition to the rule, following this 3 year dispute.
2. This was likely a very troubling time for Rabbinic Judaism. In fact, the Tur in the name of the Ba'al Halachot Gedolot codifies a fast on the 9th of Adar, which is said to mark the beginning of this great dispute. See page 3.