Washington (CNN) Hillary Clinton leads Donald Trump in the 2016 presidential race, two new polls of registered voters show -- but they differ on the size of her advantage.

Trump is emerging from a difficult phase in his campaign, including the firing of campaign manager Corey Lewandowski, anemic fundraising and widespread blowback from his party over his labeling of an Indiana-born federal judge as "Mexican" and therefore biased in his Trump University legal proceedings.

The 12-point Clinton advantage would suggest those controversies have badly damaged Trump -- but the 5-point lead would indicate he'd survived the last month largely unscathed.

Another example of the widely differing results: When third-party choices like Libertarian Gary Johnson are factored in, the Washington Post/ABC News poll showed Clinton still ahead by 10 points, while her lead shrank to 1 point in the Wall Street Journal/NBC News survey.

Tweeted Trump campaign chairman Paul Manafort: "I prefer NBC/WSJ poll."

I prefer NBC/WSJ poll — Paul Manafort (@PaulManafort) June 26, 2016

The Washington Post/ABC News poll found a number of troubling signs for Trump.

Of those polled, 61% said Clinton is qualified to be president, while 64% said Trump is not qualified.

By a better than two-to-one margin, voters said Clinton, not Trump, has a better personality and temperament to serve as president. While 50% said the idea of Clinton as president makes them anxious, 70% said the same of Trump.

And while Clinton's use of a private email server is damaging -- 56% said they disapprove of how she's handling questions about it -- Trump has been more severely damaged by controversies surrounding him: 66% say they think he's unfairly biased against minorities; 68% said his attacks on the judge were racist; and 59% disapprove of the way he has handled questions about Trump University.

The Wall Street Journal/NBC News poll found Clinton with huge leads among minorities -- besting Trump 87% to 5% among African-Americans and 69% to 22% with Latinos.

She leads with women, 52% to 35%, while Trump holds the edge among white voters at 49% to 37%; men, 48% to 38%; and independents, 40% to 30%.

"The fact that Donald Trump had a really bad period and he went down just a few points indicates that it will be difficult for either candidate to break out given the hard-set division in the electorate," Fred Yang, a Democratic pollster who conducted the poll with Republican pollster Bill McInturff, told The Wall Street Journal.

The Washington Post/ABC News poll surveyed 1,001 adults between June 20-23 with a margin of error of plus or minus 3.5 percentage points.

The Wall Street Journal/NBC poll surveyed 1,000 registered voters between June 19-23 with a margin of error of plus or minus 3.1 percentage points.