I don't think there's one universal "dark side" to working at any successful startup, not anymore than there's one "dark side" to working at any other very broad category of projects.

At best, you're going to get a laundry list of various issues people encountered at (what they consider to be) successful startups.

I'd answer the question a bit differently: the downside of working at a successful startup versus a successful mature company.

At a mature company, success is more of a uniformly good thing. There will typically be growth, people will be promoted, there will be a strong inclination to keep the current team ("don't change a winning horse") so often anyone in influential position will see increased bonuses and other benefits. Very often you can expect promotion, especially if it's a mid-sized growing outfit rather than a huge one.

In startups, "success" often means your shares are worth more on paper, but not necessarily more profit. For example, "success" at a startup may mean your userbase is exploding, but you're not making profit on each user, and perhaps even losing a bit. Like every other process, success can lead to less stable and predictable results in startups versus mature companies.

Often it will increase stress, as more successful startups are under even more pressure to keep performing, since you are now a potential unicorn. There will be a lot more investor interest, but that comes with increased scrutiny and pressure to succeed.

It's quite likely there will be changes, including personnel changes. Many startups are a wild bet at first, so they start with a "B team", a group of people whose opportunity cost is typically low, which means they're not at the top of their field and often don't have a solid track record, so they're willing to take the risk on an unproven business model. As the startup shows signs of success, investors will be willing to pay more, and the bet starts to look more promising, so "A players" will start showing more interest. Very often there will be pressure to bring such A players in to replace anyone important all the way up to the executives. This is especially true when VCs are involved, and they will often have an "A team" in mind to replace the old "B team".

So I'd summarize that success at a startup will tend to bring more pressure and a lot more risk of bad outcomes for you as an employee. For many employees, that may be a net negative. There's also a positive though: if you're considered an essential, well-performing employee, and willing to work very hard and withstand the increasing pressures, you may end up as part of the new "A team", which may get you a fat package of shares that are now more likely to be worth something. But I've also seen startups where any one who worked there so far was looked down upon as a stereotypical "B player", with even great performance disregarded and ignored. So there's potential reward, but a lot more risk.

There are also many horror stories about how getting dismissed as a "B player" at this stage also involves the owners trying to suck back every piece of equity you may have hoped to retain. Now that the equity is worth something, you'll find the majority owners typically a lot less willing to share it. You'll obviously lose any options that haven't vested. Sometimes "B players" with a lot of yet-unvested options will be dismissed for that reason alone...