If you use the same catalog file on your new system as well, then everything will be same like your edits, collections, keywords, rating etc.
Default Location for Lightroom Catalog
C:\Users\[user name]\Pictures\Lightroom\Lightroom 6 Catalog.lrcat
/Users/[user name]/Pictures/Lightroom/Lightroom 6 Catalog.lrcat
You also need to copy the Images as well in the same file structure on the new system.
Hope it helps.
Thanks. That sounds like it could be a lot of work. I'll have to think if it is worth the effort or should I stay with my present method.
Well, yes if you want to use the same catalog file then you have to copy all the images in the same file structure on the another system.
Either you can keep all the data(Lightroom Catalog & Images ) on the External Hard Drive, which will help you to switch between the computer.