https://en.wikipedia.org/wiki/Directive_on_Copyright_in_the_...
A big difference is in the boundaries. GDPR is bounded by your customer records. One customer, one collection of personal data. There's a hard upper limit: about 7 billion. Companies tend to scale with customers, so generally bigger companies will have bigger customer bases and bigger employee bases to handle protecting the records.
The Copyright Directive's bounds is user content. One customer, any number of potential infringements. A single person can run a company with 100 customers who upload 10,000 images each per year. Managing the customer base is pretty easy, managing the data storage is pretty easy, GDPR-protecting 100 people's data is pretty easy. But 1 million potential copyright infringements per year, each one of which could even be claimed by multiple rights holders. Your risk exposure grows with data, not with people. That one-man show probably can't handle tens of thousands of take-down requests, nor build an AI Machine Learning Cloud Native Copyright ID Blockchain System to automate it.