Change yes but not for the average joe.
The most likely result IMHO is an agreement between the EU and the USA. The result could be a test for EU federalism.
US corporations work in the EU via a variety of legal structures designed to lower tax and limit liability/risk. They have managed to profit nicely despite changes to EU and local law by just staying ahead of the very slow legislative process and lobbying. Similar methods will be used to architect legal data transfer.
I admit it is fun to imagine this turning into an exciting change. So riddle me this:
How does an EU citizen act against a non-European & non-resident company doing bad things with their data today?
All of the UK is not in the EU, what happens if an EU person's data makes it to the USA via the Cyprus Sovereign Base Areas or British Indian Ocean Territory?