To add on to what kohanz said, I think it is important to find out concretely what "more autonomy, using more exciting tech, solving bigger problems, working with movers & shakers, and generally more of a challenge." mean exactly in terms of this startup.
Let me explain:
1. What does more autonomy really mean? Do you have product level decisions? Do you have decisions governing the architecture of problems? Do you have the kind of experience that means they will eventually trust you with that?
2. What does more exciting tech mean? Is that a question of you using a new technology, new paradigm or new space? If so, have you considered what will happen in a year's time when the tech is something you get used to? Also, if more exciting tech means the prospect of working on fancy new tools all the time, there is a drawback to that too. As a company grows, you have these bits and pieces which don't fit correctly and don't scale properly.
3. 'working with movers & shakers': Again, it completely depends on the company what this means. Being able to sit next to your CEO or grab a beer with him could mean nothing more than a 1 degree connection on linkedin or something, it all depends on how they perceive you too.
4.'solving bigger problems': Again this completely depends on the company's scope. Scaling up a web app to ten thousand users at a startup vs working fresh out of school in Amazon scaling up to millions and millions of users are two different sorts of bigger problems.
A few years back I was faced with these two caricatures of companies two: a startup being a romantic place where a bunch of cool people sip beer and change the world and big companies filled with engineers who dress in blue shirts and slacks and are generally "cog" in a wheel. Again, the truth is that every company is different.
Oh, yeah, I can't agree more with what _kohanz_ said there. Team matters more. In fact, when I make my decisions, I would care more about the team than whether the company is considered "prestigious" or "exciting".
Also, lastly, unless you are interviewing with an early stage startup, asking the startup to be relatively competitive is not out of the realm. I know there is this perception in industry that working in a startup automatically means lower pay but that doesn't always have to be the case. There are tradeoffs always obviously, in that a small startup won't be able to say match Google's benefits or whatever but having said that, you can surely make sure that your family is not left high and dry if things blow up.