Keep in mind you're comparing an off-the-cuff quote to a carefully worded marketing slogan.
I think I found a way to put it differently: in one case it is the user that lets the company collect the data, in the other case it is the company that lets the user collect the data.
To make the data equivalently useful, I would want to make it the most complete - so asymptotically I would get the same data set collected in both cases. But if this all is done with my consent, I would feel more in control about it - even if "yes to all" is more efficient for me.