In a way, it's a false dilemma. The correct answer is to not ask them to. In a perfect world, your second adventure would grow organically out of your first. Players of Keep on the Shadowfell would be drawn into the next story by a direct threat to Winterhaven, or by a desire to continue their crusade against the cult of Orcus, or through pursuit of the specific priorities their character has developed over the preceding sessions of play.
Thunderspire isn't having any of that. It wants players to get to its Labyrinth as quickly and efficiently as possible and it's not really concerned how that happens. A charitable view sees the module as wisely focusing on its core content, but there's no real dispute that in skimping on its hooks it's doing itself a disservice.
Thunderspire offers four key hooks to get player characters involved in its story. The first is entitled "Investigate the Bloodreavers". The Bloodreavers, if we remember back to Keep, are an organisation of hobgoblin slavers based out of the distant Thunderspire Mountain. The hook involves the players taking on the role of self-appointed slave police in order to look into the unfocused and fairly nebulous threat presented by this organisation. Those investigations will lead them quite quickly to Thunderspire, which is where our story begins.
If the players aren't quite the zealous vigilantes contemplated by the hook, the module provides for Winterhaven's Lord Padraig to offer up a 1,000 gp reward for the head of the Bloodreavers' chief. There's an unfortunate escalation here; in Keep, Padraig could summon a mere 100 gp to pay for the extermination of kobolds who were directly threatening the village; now he's got access to ten times that to spend on hunting down a group who are, on any fair view of it, Someone Else's Problem.
A more pressing problem with the Bloodreaver hook is that while it gives players a reason to tackle the first of Thunderspire's four mini-dungeons (the Chamber of Eyes), there's no through-line to keep them progressing on to the rest of Thunderspire's content. If your group is characterised by a mercenary nature or merely keen practicality, it's open to declare the adventure over after defeating the Bloodreavers in the story's opening act.
The second of the hooks is worse still. It's called "Trade Mission" and it's what computer gamers refer to as a "fetch quest". Winterhaven shopowner Bairwin asks players to make a delivery for him to the Seven-Pillared Hall, the small bastion of civilisation hidden beneath Thunderspire. Once again, this will occupy players long enough to get them to the adventure location, but then give them no reason to tackle any of the mountain's challenges. Also, the Forgotten Realms conversion for Keep re-cast Bairwin as a secret cultist of Orcus, so for groups that have used that article Bairwin may well be long dead.
A third hook, "Call to Adventure", is so brazen as to be almost deserving of respect. It amounts to little more than Winterhaven sage Valthrun telling players that Thunderspire is kind of an awesome place, in which they will probably find adventures. I quote:
Valthrun doesn't have any additional information, but he longs to convince a party of adventurers to explore the place and bring him back firsthand news. "Such wonders you will see," he keeps on repeating. "Such wonders, I am sure!"As hooks go, this is on a par with the DM declaring that the next adventure is going to be in Thunderspire and asking if anyone has a reason not to go there.
The last hook is the real meat of Thunderspire Labyrinth and is ultimately so critical to making sense of the module that it should have been highlighted as compulsory. It's called "Slave Rescue".
As we know, Thunderspire plays host to the Bloodreaver Slavers. In "Slave Rescue" the Bloodreavers have recently captured a dozen slaves from a nearby village and absconded with them to the mountain. The players are engaged by a local do-gooder (the module suggests Winterhaven's Sister Linora) to pursue the slavers and rescue their victims.
The reason this works is that the slaves provide the module's much needed through-line. When the players confront the slavers, they find the slaves have already been sold to a nearby duergar faction. Attacking the duergar (located in a second mini-dungeon) results in the liberation of most of the slaves, but also reveals the depressing news that the last two of the captives were on-sold to a gnoll band for use as human sacrifices. A desperate pursuit of the gnolls leads to the third of the module's mini-dungeons, and eventually reveals the identity of Thunderspire's master villain.
There's an opportunity here so obvious that it's amazing the module misses it. What none of these hooks provide is a personal connection between the players and the adventure. As-written, the best-case scenario sees players motivated by a combination of greed and do-good-itude. To make Thunderspire a genuinely compelling game, you need to provide a reason why these problems are the players' problems.
It's as simple as personalising the captured slaves. The faceless villagers abducted by the Bloodreavers can just as easily be the PCs' family, friends, or even the entire named population of Winterhaven. Such a simple change instantly transforms a quest into their quest and gives them a unique and dynamic stake in the outcome of what follows.
In a worst-case scenario, if all you manage to do is coax players into visiting Thunderspire, you can at least be confident that once they get there, they'll find plenty to do.