Should I upgrade the old Macbook pro to the same mac osx version as the new Macbook Pro prior to migration?

Hi mamosthlm,

Thanks for coming to Apple Support Communities for help today with Migration Assistant and updating your old Mac before migrating.

It's not necessary to do this. However, you may want to in order to check app compatibility before the initiating the process. Please see: How to get old versions of macOS.

Also see: 32-bit app compatibility with macOS High Sierra 10.13.4 and later.

Have a fantastic day!