Startups in my opinion are almost never a good deal for folks who have the option to join a big successful company. My points will be directed at folks who can get a job at a big company easily but are lured by the great things they've heard about startups. Specifically I'll target the issue of compensation.

Startups, in my experience have very shady predatory compensation strategies. Along with the VCs that fund them, startups target people fresh from college, selling them the "each stock COULD be worth X, so you could be worth Y" story. They also target people who have spent their entire career at startups since this fairy tale works on them too. I have worked at both startups and big companies and my compensation at bigger companies has been so much better. People working at startups don't believe me when I tell them how much I make. Past me would not believe present me either. I am not talking about a 10% or 20% or even 50% increase in compensation. My pay is 4.2x of what it used to be and I know people who have had similar experiences. It's not like I was being paid peanuts at the startup I was at either. The pay at big companies is just much much better. It's easy to underestimate the power of performance evaluation driven stock refreshers and the sheer increase in the stock value that some of the big companies have had. Here are some things one should consider compensation wise when working at a startup:
* You are essentially getting a lottery ticket with your stock options. How do you value this lottery ticket? Don't buy the stories the founders sell you on how this is a gazillion dollar market and even getting a faction of it would make FooBar a trillion dollar company. A simple but still optimistic method - just use the VC valuation. They have way more information and experience than you do and if they value it at X, it's at best valued at X. So if your tartup decides to give you 0.25% of X then you're stock is worth 0.0025X at best. You'll be surprised how little your options are worth if you use this method.
* But even that valuation is optimistic. If you leave the company before they go public (or hit another liquidity event) you either leave with your existing options and pay a tax bill on something that may be worth nothing OR you leave with nothing. Now some startups let you claim your options for up to 9-10 years after you leave, but the typical ones give you a period of about 3 months - so you're forced to make this decision. The irony is that if your startup has actually done well, the tax bill might be too big for you to pay and you have no option but to stick around or leave with nothing. I've known cases of people who have poured their heart and soul into a startup, got burnt out and then were laid off and had to leave with nothing. Consider how long it takes the successful startups to go public these days and add a risk factor to your valuation based on that.
* Okay, so you're rich enough to afford the tax bill on your risky options when you leave - you might still get screwed. Guess whose shares are getting diluted the most during the next round of funding? Ex-employees have no say in the company and the company has little to no loyalty towards them. A company could easily do something shady like raise money, dilute current and ex-employees, but give all the existing employees new shares to make up for the dilution.

For a sample of some of the disingenuous "I know what you need better than you do" kind of marketing that VCs do to help maintain the status quo, take a look at https://a16z.com/2016/06/23/options-timing/. These folks are not your friends.

Startup founders get the vast share of the equity and even the 3rd or 4th employee gets a tiny fraction, while having to do the same amount of work. So if you still want to work at a startup, my advice would be to either be a founder (hopefully not one that continues the cycle of screwing over other employees) or at the very least come from a big company. Founders and VCs know that big company employees make a lot of money and they wouldn't just give up on their good compensation package for the "each stock could be worth X" story. Hence they compensate them much better than their average employee that doesn't know the market. Folks coming from bigger companies can also afford the tax bill associated with early exercise of options or exercise of options when leaving a company. Further consider working at startups where they let employees buy their options years after leaving. There are also successful startups that straight up give RSUs.

The well known article by Dan Luu at http://danluu.com/startup-tradeoffs/ addresses some of the other points raised when discussing the relative meritcs of startups VS big companies.