If the start-up fails and you suddenly find yourself without a job, will that cause you incredible hardship, or just a minor inconvenience?
When looking at the issues, you need to look clearly at the possible risks also.
It may help to look more carefully at the start-up and determine how feasible their business plan is, are they counting on some miracle to happen, or do they have the funding to last about twice as long as they expect it will take?
Even for a medium sized company it helps to look at how well they are doing, but you are less likely to find yourself unemployed without any severance than from a start-up, if they completely run out of funding.
You may want to look at the type of people you will be working with to determine where you may learn the most.
How involved are you going to be with the design or business side? How will your work be different at the startup than at the medium sized company? Is it basically that you are expected to work ridiculous hours for a nice salary, but in the end you are just developing software, for example?
A startup can be a great experience, or it can be a very painful lesson, which one is largely going to be based on you trying to understand the issues as much as you can, and then making the decision with your heart.