Before I begin, I will admit this is highly dependent on different circumstances within each start-up, and the growth potential of your specific company.
However, I am making the case that start-ups are better than any BB or established firm due to a couple of main reasons-
1) Exposure- Start-ups by nature are way smaller than your average company. Chances are, you'll know every coworker in your office and what they do. Given the nature of start-ups, there are a lot of processes that aren't clearly defined, or have a lot of room for improvement. You'll gain exposure to many different types of jobs, as opposed to being pigeon-holed to a specific task working for a bigger company, and you'll have a direct role in improving a lot of these different processes and having a tangible impact on the efficiency of how your company runs. In addition, the proximity and exposure to senior management can't be overstated. I entered my company as an intern, and was able to have regular conversations with the COO and CFO everyday about different tasks I was doing, and was able to provide real input on a variety of different projects.
2) Growth Potential- The ability to advance through the ranks is seemingly unmatched within a start-up vs a traditional BB. While promotions in a BB might be a game of kissing ass to your boss, staying late in the office, and hoping to stand out from the 20 other people with the exact same job and credentials as you, promotions in a start-up are different. Because of the exposure you have to all your coworkers (especially senior management), your value to the company will quickly become apparent, with the work you do all having tangible benefits for the company. If you are a standout worker, you will get promoted extremely quickly, especially since they won't want to lose you to one of these said BB type roles.
3) Pay- Piggybacking on the above, with fast promotions come fast pay bumps. For me personally, I started off as an BO type intern making 15/hr. Once I graduated, my starting salary was 70k base . About 9 months later, I got a raise to 80k base, and another 4 months after that, my base is now 85k in a front office type role. With bonus factored in, I expect to make around 105-110k all in for 2019. The total timeline between when I started as an intern until now has been a little over 2 years.
4) Skills gained- Because of so much responsibility and exposure to different types of jobs, I have gained skill sets in a variety of different roles that give me a lot of exit opps if I choose to do so.