The centralization of the web is what worries me. I suppose non-neutral net can contribute to that, but even with a neutral net we've seen extraordinary centralization around a few major sites. Will neutrality really save us?
That is because neutrality creates a (somewhat) level playing field. Without it, Facebook could, theoretically, pay Comcast to slow down a new competitor that is just emerging.
I say "theoretically", because such an action, if taken overtly, would probably still run afoul of competition law. But there will be other, more subtle, ways to achieve similar results. I would expect the result to be worse for data-heavy and latency-sensitive applications, as well as anything using a non-standard protocol (i. e. peer-to-peer networking etc).
It's possible, although not certain, that current service levels might remain accessible for new startups. But any future improvements would be tied to signing contracts with any provider whose customers any new startup would want to reach. Prices will tend to be exactly the value of these customers to the startup, minus one cent–or as close to that as can be measured.