Zillow is not accurate at all. In my market, Redfin has been accurate to within 5% of the price, up or down. However, Redfin is a real estate agency, so they use their estimates and have access to data that Zillow doesn't, and they will adjust the algorithm at a neighborhood level.
Zillow is merely a real estate value estimator (they don't use sufficient data to earn the right to call themselves an appraiser nor do they provide sufficiently updated listings to justify calling them a listings service).
