They're both "correct", in so far as predictions can be. They're measuring different things.
FiveThirtyEight has three models, with the default one at that site being the "polls-only" one. They go into their methodology here, and summarize it:
Step 1: Collect, weight and average polls.
Step 2: Adjust polls.
Step 3: Combine polls with demographic and (in the case of polls-plus) economic data.
Step 4: Account for uncertainty and simulate the election thousands of times.
In other words, it's purely data-driven: Polls + demographics = prediction.
Predictwise, on the other hand, aggregates "Prediction Markets (Betfair, PredictIt, Hypermind), Polling (HuffPost Pollster), [and] Bookie (OddsChecker).". Their method is described as
Step 1: construct prices from the back/sell, lay/bid, and last
transaction odd/price in the order book. We always take the average of
the highest price traders are willing to buy a marginal share and the
lowest price people are willing to sell a marginal share, unless the
differential is too large or does not exist.
Step 2: correct for
historical bias and increased uncertainty in constructed prices near
$0 or $1. We raise all of the constructed prices to a pre-set value
depending on the domain.
Step 3: normalized to equal 100% for any
mutually exclusive set of outcomes.
In other words, it's mostly market-driven: People's bets -> Market -> Prediction. (In theory, there is polling data used in there, but I can't find any details on that.)
FiveThirtyEight is predicting how people will vote based on polls and demographics. Predictwise is aggregating who people think will win based on market data. Two different methodologies to produce two different statistics, resulting in two different percentages.