(I've posted this in more detail before.)
Essentially all the real problems the Network Neutrality proposals try to address are misuses of technical capabilities (which were designed to enable improved network performance) to implement anticompetitive or consumer fraud schemes.
The FCC is good on technical issues, but is generally rotten on consumer protection. This is not a technical issue, and technical tweaks to address it also tend to re-break the network issues it was built to fix. Expect trouble if you try to fix this stuff via FCC regulation.
The FTC is a consumer protection agency with a track record of taking on large companies (including technical ones - AT&T, IBM, Microsoft, ...) often imposing serious beatings that mitigate or solve the problems or at least mitigate them for years or decades. IMHO they are the agency that could handle the job.
They'd also like to handle it. But right now there are two issues: They read the law as blocking them from ruling on the Internet, and they are currently underfunded and understaffed for the task.
IMHO the FTC seems the right agency to handle the job, while the FCC seems like to break it worse rather than fix it once they're turned loose on it. It would just require a legislative tweak to make it clear they have a go-ahead, and perhaps a bit of appropriation to staff them up.
Much as I hate to encourage government interference of any sort, if you intend to pass and enforce laws to turn the dogs of law enforcement loose on miscreants, you should turn loose the breed of dog that has a track record doing the right thing.