Clinton versus Trump

net neutrality

Clinton's for it, Trump's against it.

nationalizing the healthcare industry

Hillary Clinton's official position on health care isn't nationalization, but includes a public option and promoting Medicaid expansion. Donald Trump parrots Republican talking points, focusing on a repeal of Obamacare with some free-market-based suggestions. So I don't think "their stated opinions are the same".

Even if you disregard Trump's written position in favor of the various contradictory opinions he's expressed over the campaign, and somehow draw out of them an equal or preferable position to Clinton's - in practice, Trump will be working with Republicans in Congress and Clinton will be working with Democrats. Though he would have some influence of his own as president, he's hardly a complete renegade; aside from the above link, among other things, his official tax plan is based on the House GOP's, and his list of potential Supreme Court justices includes your typical conservatives. Needless to say, the Democratic and Republican parties as a whole have rather different opinions on healthcare nationalization.

re-nationalizing the prison industry

Trump has voiced support for private prisons; Clinton wants to end them (search for "privatization").

expanding education funding

Clinton's wants to fund K-12 (by expanding 'Build America Bonds'), debt-free college, and preschool and assistance for student parents; Trump has a plan involving block grants, which would probably replace (and reduce) existing funding, and he has previously repeatedly suggested cutting the Department of Education.

and establishing modern educational techniques and certificates of attainment

Not enough detail here to determine whose education plan (aside from funding) you'd prefer, but they're certainly different.

using our existing anti-trust laws like a ban-hammer

Clinton has suggested "beefing up the antitrust enforcement arms of the Department of Justice and the Federal Trade Commission". Trump... who knows. Apparently he wants to use antitrust to go after the Washington Post because they "treat him unfairly".

extending employee protections

Clinton supports it. Trump doesn't seem to have much of a position, but his party certainly opposes it.

reducing the length and severity of patents

Neither candidate supports this itself, but Clinton's plan includes measures against patent trolls and ensuring the PTO is properly funded to, among other things, "ensure that only valid patents are issued".

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