In a surprising twist, newly announced Democratic vice-presidential running mate, Kamala Harris, has a higher net personal rating than either Trump or Biden.
Many of those polled said their decisions were motivated by anti-Trump sentiment.
Fifty-eight per cent of respondents who said they would vote for Biden indicated that their choice was driven by opposition to Trump rather than support for the challenger.
On the other side, 74 per cent of those backing Trump said their vote was in favour of him rather than against Biden.
"In one respect, Biden's vote looks like Trump's did in 2016: more a vote against their opponent than support for them," Jeff Horwitt, another Democrat who worked on the poll, told WSJ.
"Clearly, Biden is in the lead. Clearly, Trump has a lot of problems," said Hart, who conducted this survey with Republican pollster Bill McInturff.
But Hart stressed that the election is "not a done deal," especially with a majority of voters saying they're either uncertain or pessimistic about the job Biden would do as president.
"Biden is well-known, but not known well, and people are looking for direction on that," Hart said in previewing the upcoming Democratic convention.
Democrats are hopeful that this week's nominating convention will help bolster Biden's popularity among the party by highlighting his strengths as well as his VP pick, Kamala Harris.
However it's unclear how much impact this year's conventions will have for either party as they will be held via Zoom due to coronavirus concerns - stunting the usual lively atmosphere that energises voters.
The Republicans are set to hold their convention in the week beginning August 24. Trump fought to keep the event in-person but ultimately folded under pressure from experts who said it wasn't safe to hold such a large gathering.
The WSJ/NBC News poll was conducted between August 9 and 12, prior to Biden announcing Harris as his running mate.
However the poll did include some questions about Harris as it was widely speculated that she would join the ticket.
Meanwhile a CNN poll showed Biden's lead over Trump among registered voters has significantly narrowed since June.
Overall, 50 per cent of registered voters back the Biden-Harris ticket, while 46 per cent say they support Trump and Pence.