Hey there, @Chri3s.
Thanks for taking the time to reach out to the QuickBooks Community for support.
For now, you'll need to enter the address for both vendor and customer sides. At this time, there isn't a way in QuickBooks Desktop to share information between vendors and customers. Although you know that they are the same person edited differently (vendor, customer), QuickBooks reads them as separate accounts due to the need of the { } at the end of each name, therefore, making them have different names (different people).
I understand the importance of sharing information between customers and vendors and understand that adding a customer as a vendor would be much more efficient for you and your business. I've gone ahead and submitted this suggestion to our Product Development Team. This way, the feedback can be considered for a future update.
Please let me know if you have any questions or concerns. I'm always here to lend a hand. Take care, Chris!