How thorough is Migration Assistant?
Migration Assistant does truly copy all your user data from the old computer to the new - that includes Parallels virtual machines and your settings.

Migration Assistant does not copy over the actual operating system, as you already have that on the new computer (i.e. there would be no point in copying it over). Similarly Apple supplied standard programs (such as Safari) are not copied over - but you would already have those on the new computer. Settings, bookmarks, passwords, etc. for Safari are copied over.

In essence if you just want to copy over all your data and settings and continue working your new computer - Migration Assistant will work for you. However, if you want to downgrade your new computer to an old operating system and old versions of Safari or similar - then Migration Assistant alone cannot do that for you.

I have personally used Migration Assistant for 15+ years when moving from old to new computers, etc. - never had any problem with anything missing.

You can read Apple's guide on using Migration Assistant here:

https://support.apple.com/en-au/HT204350