Hi There,
Thanks for writing us and I hope this message finds you all amazingly well! While we generally try not to make direct comparisons to competitors, we do love speaking on Moz. Moz is generally excellent because we will actively manage the listing for the course of a year, so edits and to the listing are a part of an annual subscription. After taking a look into Bright Local it seems that they are a monthly service and may have a different policy on edits and changes.
David Mihm does an awesome job of covering some of the advanced reporting available in Moz Local. https://moz.com/blog/announcing-local-reporting
I would review that and hopefully other users who have encountered Bright Local in the past, can better speak to the services they provide.
In the meantime if you have any questions for me let me know!