I use airnow.com. The site's usability is fine, and more importantly, their AQI numbers look much more realistic than the data you're getting from PurpleAir. You might consider another data source.
Can you share the rough location where you see a discrepancy? There are various data quality issues with PurpleAir that I attempt to clean up, but after cleanup the data seems to agree pretty well. They seem to have a lot more sensors than AirNow uses so in some cases they can see more localized pollution issues.