There are several things to consider here.
1. Powerschool is not just a gradebook and it is not an LMS. While it offers grading and that is a part of it, Powerschool also handles demographics, reporting, state reporting, discipline etc. Powerschool is designed as an SIS, which Moodle is not. So, bear in mind that Moodle and Powerschool, while they cross over in areas, handle different things for the most part.
2. If you are thinking of just switching the gradebook over to Moodle, while I love Moodle and all that it offers, I can tell you that you will have a lot of very unhappy teachers. Moodle's gradebook has undergone a huge rewrite and has improved hugely from its meager beginnings, but Powerschool is far superior in its grading interface. Also, I will presume that attendance will have to stay in Powerschool and teachers are not going to want to keep jumping between the two.
Having said all that, I originally started with Moodle for its grading capability and use it exclusively for our Distance Learning classes. Students have to log into Moodle because their assignments are posted there but they also see their grades for those classes. If you were able to set it up so that their grades were posted in Moodle initially and imported to Powerschool later, that might prompt them to get into Moodle for early grade access.
You have my two favorite systems there. If you want to hang on to Moodle, I would talk about the pains of learning a whole new system. If students are not accessing Moodle, it is because they don't have to and that is because the teachers are not using it. The same will most likely happen with whatever LMS you use.