It really depends on what role you're looking for. The "data scientist" label gets attached to a lot of different job descriptions, some of which Ph.D. training is more useful than others.
Over the course of a Ph.D., you will likely develop a number of skills that aren't often emphasized in undergraduate (or even masters-level) study:
Navigating relevant literature: Finding useful papers and extracting the meaning from them is something you'll get a lot of practice in while writing your thesis.
Defining a clear methodological problem to solve: All these will have to answer a question, but figuring out which question to answer can be one of the most difficult parts of Ph.D. research - you need to find a problem that's interesting, relevant, and novel, but also solvable in two to five years by someone with (probably) relatively little research experience.
Applying theory to know when a method is appropriate: There's a great quote that "knowing the difference between tight and loose tolerance is perhaps the most important measure of a craftsperson". The theoretical training over the course of a Ph.D. helps to develop a deeper understanding of why certain methods work, and how damaging it is to violate the assumptions of each model. A master's degree gets you some of this training as well.
That said, a Ph.D. typically takes five to seven years post-undergrad (or three to five years post-master's). There are also important skills and attributes that you'd be more likely to build up during that time in an industry setting:
Taking a pragmatic approach to problems: You can't live as much by the 80/20 rule when it comes to academia. A huge amount of effort is spent on the final polish for an academic paper, and as such PhDs tend to lean a bit too far towards perfectionism when they first come out of grad school. In industry, you also typically select a method based on the problem, while in academia it's sometimes (not always) the method that comes first.
Awareness of your specific industry: Deep knowledge of the nuances of the problems and demands of your chosen industry is (unsurprisingly) something best built on the job.
People skills: A lot of Ph.D. work is solitary, or done only with a small number of colleagues. Soft skills like mentoring, running meetings effectively, and building consensus are more easily acquired through the more collaborative settings that you encounter in industry.
As you might expect, the Ph.D. skills are more important if you're aiming for a research-oriented data science position that involves the development of novel methodology. It's also worth considering that some companies are also unwilling to hire post-undergrad for data science roles or promote them beyond a certain level in an IC track.
All that said, there are large swaths of data science that don't require these research-oriented skills. There's a huge amount of impact that you can have by leveraging the skills that are better built through industry settings as well. I'd recommend looking at job postings for the kind of work you want to do and talking to data scientists with and without graduate degrees in order to figure out which direction is best for you.