Windows 10 on both, it seems.
Try "copying" *all* .PST files from the Outlook 2010, to Outlook 2016. It may be that simple, though I suspect it will involve some difficulties above that simple a level of procedure.
In reality, the 'copying' would be like this:
on the old laptop, do a
File - Export
of all PST files, to an Export file.
then on the new laptop, take those Exported files, and
Open & Import - Import
them into Outlook 2016. This will transfer emails, mailboxes, contacts, and calendar.
Try it and let me know of any difficulties, please. Thanks.