I'm going to dismiss for a moment whether Sanders or Trump are in fact establishment candidates, as one is a man who has been in Congress for over 25 years and the other is a billionaire real estate mogul who has more money than all but a handful of Americans. Let's assume for a second that both of them are right, and that they are not the establishment, and that Hillary Clinton is (she's also protested on this front, saying that her gender makes her anti-establishment, but I think even she knows that as a former First Lady, US Senator, and Secretary of State who is on her second run for the White House, that argument isn't going to keep the boat afloat). Both men are arguing for weirdly similar platforms in the terms of the "government is not looking out for you," variety (which may be why some like actress Susan Sarandon think that Trump is preferable to Clinton, though I again would like to hear that line of thinking from someone who isn't a multi-millionaire) but wish to fix that problem in totally different ways. Trump wants to remove government regulation to improve conditions for a free market, a relatively reliable conservative trope, and thinks we should start to eliminate a number of trade agreements (the Republicans are less inclined on this one, though trade agreements are so unpopular on both sides of the aisle it's hard to tell here at the moment). Sanders also wants to eliminate trade agreements, but wants to put more regulations on the banking and finance industries in order to ensure that everyone has a relatively level income, or at least a sound opportunity toward it. Clinton is admittedly somewhere in the middle, but more toward the Sanders camp than Trump's.
The idea of the "non-establishment candidate" is that they will be able to come into Washington, which is chronically dysfunctional, and through their elevated ideas and bold new vision, change what is fundamentally broken about the city. Where the problem here lies is that the anti-establishment argument has been the lifeblood of politics since the mid-1970's, and it almost always wins. The reality is that since Gerald Ford was president, we have had four governors, all without any time spent in Congress, and a first-term senator with no other DC experience who ran very hard on the "Washington needs to be fixed" banner. All five of these men ran against Washington, and the American public ate it up. They came from a diverse run of backgrounds (peanut farmer, Hollywood actor, son of a president), but they all promised to change Washington.
The thing is, though, that they didn't. None of these candidates actually changed Washington-Washington bucked them and made them play its game. Some of them did it more successfully than others (Ronald Reagan in particular, but also Bush and Obama thanks to their party holding power during some of their term), but all of them ended up playing the Washington quid pro quo, certain rules aren't touched sort of game.
So it's worth examining if perhaps this non-establishment argument is faulty, and we need an establishment candidate in the White House. Tina Fey humorously once said, "politics and prostitution are the only two occupations where inexperience is considered a virtue," but the cheeky meaning behind that joke is that we should look to an experienced individual. During the 1960's and 1970's we saw some of the most radical and meaningful legislation of the last half century, but that was because we had two of the biggest Washington insiders ever (LBJ and Nixon) in the White House. You can say a lot about their morality or their connection to the common people, but a great bulk of what they promised the American people on the campaign trail they delivered, and they did so due in large part to their Capitol Hill connections. George HW Bush, the only candidate since Ford that I'd argue would qualify under the banner of an establishment candidate, did get a lot of things done from his platform in his first two years, making Points of Light happen, passing a number of environmental policies, the Americans with Disabilities Act, enabling looser gun restrictions, and his Immigration Act of 1990, all of which were strong parts of his platform in 1988. He was also, it should be remembered, wildly popular during the first few years of his presidency thanks to the Gulf War and an effective role in the White House (one with a bit of compromise on both sides of the aisle as you'll note very few people today would agree with all of those bills, including myself), and would have won reelection had it not been for a suddenly sagging economy (which had more to do with Reaganomics than anything a President Bush enabled, though of course as his veep he was rightfully blamed).
I doubt we'll see Hillary Clinton out there trumpeting the idea of "support the establishment," but it might at least be worth investigating the more experienced candidate at least for once, and she has made that part of her campaign. I know a lot of Bernie Sanders supporters have disliked Clinton, but there is a silver lining here-there will be no learning curve, and no "let's meet the leaders of Congress" situation for Clinton in January of 2017 should she be elected-she'll be able to take advantage of every single bit of her first 100 days. It'd be an interesting counter to the prevailing (and repeatedly victorious) argument that you should get an outsider to fix Washington, even if they keep repeatedly failing in changing the fundamentals of the city.