Lets divide this shall we.
NOTE: This is mostly Pre-WoW information, since we can't really compare quest quality between Horde and Alliance in WoW. That would be a tiresome and impossible task.
The Horde
Orcs
The strongest of the "five" in terms of lore and character importance. The "Old Horde," the slaughtering of the Draenei, the First War, the Second War, lethargy, the rise of Thrall, exodus to Kalimdor, the fight against the burning Legion, the founding of Durotar, WoW. A plethora of notable characters like Ner'zul, Gul'dan, Orgrim Doomhammer, Durotan, Thrall, Broxigar and other with detailed history and memorable storylines. Absolutely essential for defining Warcraft's unique fantasy feel.
Tauren
Introduced in Warcraft 3: Reign of Chaos, the Tauren haven't really excelled in some "lore-rich" race, apart from several appearances in Horde related novels, and characters of great importance like Cairne and his son Baine Bloodhoof.
Trolls
A vast (mostly undocumented) lore spanning from the Rise and Fall of the Amani Empire, to the partnership in blood with the Orcs in the Second War, the Trolls have been featured through their powerful and cunning leaders (Zul'jin, Vol'Jin, etc) and have also served as a "supporting race" in the shaping of the Horde's lore.
Blood Elves
The former Highborne, banished form their homeland, have a rich detailed history, starting with their first settlements on the far shores of Azeroth (after the great Sundering), the creation of the Sunwell, the first contacts with the younger races (the Humans of the ancient Kingdom of Arathor), their early teachings of Magic, the Alliance with Men and Dwarfs against the Horde in the Second War, the destruction of Quel'Thalas by Prince Arthas Menethil and the Scourge, their re-emergence as the Blood Elves, the trip to Outland and WoW. Lots of supporting and main lore characters such as Prince Kael'thas Sunstrider, his father Aestherian, the sisters Winderunner, and others who helped either the Alliance or the Horde in one manner or another.
Forsaken
Former servants of the Lich King, their lore is tied to that of the corpsefied citizens of Lordaeron now under the rule of their Queen, Sylvanass Windrunner. Apart from a campaign in Warcraft 3: The Frozen Throne that featured the creation of Syvalansses new kingdom, up till WoW, the Forskane to not really thrive on lore or many significant characters (perhaps maybe, Varimathras but he and his brothers were part of the Burning Legion).
The Alliance
Humans
The Horde equivalent in the Warcraft universe. Similar to the Horde's own beginnings, the Humans have a rich lore and many notable characters that are recognizable even outside Blizzard's own games. The rise and fall (and rise) of Stormwind, Kharazan, the Second War, beyond the Dark Portal, the Third War, the battle against the Burning Legion, Old Hatreds, and WoW. Each human character, starting from Lothar, Khadgar, Tyrailon, Medivh, Prince Arthas, Kel'Thuzard, Uther, and many, many others have brought the other side of the coin, the "righteous, yet easily deceived" nobles who have lost much but gained little in their own definition of history."
Night Elves
One of the oldest, the wisest, and most prominent (newer) race to the Warcraft universe, the Night Elves or Kaldorei have been the main protagonists in many stories and novels, ranging from the War of the Ancients, to the return of the Burning Legion. Their heroes and villains like the brother's Stormrage, Tyrande Wisperwind, Maiev Shadowsong, and others have pulled the strings in major, lore changing events.
Dwarfs
Similar to the Trolls in terms of significance, the secluded yet always present Dwarfs have flourished in terms of lore and storytelling in recent WoW history, yet little was known apart from their War of the Three hammers and their kingdoms in the Warcraft universe.
Draenei
The "youngest" race to join the Alliance, plays a significant role in WoW, though it has a lesser impact on the Warcraft universe before it. Not many stories and novels have surfaced with Draenei as a notable character, though there are experts and books that take place around some of the conflicts the Draenei have been part of.
Gnomes
WoW- related mostly.
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So, the verdict:
The Horde in terms of characters, better history and more violent past/corruption.
The Alliance in terms of sheer content and characters.