I would think that it depends on how you will use it.
Are you going to drive it every day? If yes, no question in my mind... update it to make it safer for the road, and more comfortable for the driver and occupants.
Are you going to look at it and take it out on a Sunday cruise on a nice sunny day, or park it in a museum? Restore it to stock condition.
Is money too much of an issue? Then find a running engine and tinker with what is there. Keep tinkering, and then tinker some more. Do the mechanical first and paint it last.
I hate to see them rebuilt to the point that they can't be brought back to stock. If you do change it, you might want to keep your old parts for the next owner.
Do what YOU want and believe that you are building what you want in the end.
