A piefed migration allowed the possibility of backing up every post, but it only shows up on the piefed instance itself, the old backed up posts don't federate out.
Had Perish migrated to a Lemmy instance, there would be no backup at all, and we'd have to start from scratch. The only backup of the community would exist as the old posts from lemm.ee that exist on other instances.
Yes, they're 100% cross compatible. As an example, you can access !piefed_meta@piefed.social from your Lemmy instance seamlessly.