I've also walked both, and echo what the others say above. A couple of more differences: Most obviously, everyone in England (even the foreigners) will speak English. That won't be true in Spain. While both trails feature lots of ups and downs, the C2C is almost entirely on real trail or dirt paths, and can be quite rugged, especially in the first part across the Lake country. By contrast, a good 50% of the Primitivo is on asphalt.
And while this is largely subjective, as a pure walking experience the only things in my experience that have rivaled the C2C are treks across the Dolomites in Italy and the Sierras in California. So while the Primitivo is wonderfully scenic, the C2C is another order of Wow. (Again, purely my subjective point of view).
Other things: unless you're wild camping, the C2C cannot be winged. You'll need to reserve everything (months) in advance. You can readily wing the Primitivo, or just reserve a day or two ahead. Far fewer hostels on the C2C, and everything will be a lot more expensive, as Antonius notes above.
Navigation on the C2c will be more of a challenge, as the English don't seem to believe in signposts that much, so a track on your phone will be of more use (though this might be better now, as the C2C was recently denominated a national trail).
But let's not forget the rain. We had 16 out of 17 days of rain on the C2C in May - June, 2019, no rain in 14 days on the Primitivo in 2017. Obviously, the weather fluctuates a lot, but it's almost a certainty that it will rain more in northern England than in northern Spain.
But overall, I'm with Anthony Rocco: 5 stars for both, and both incomparable. Just different.
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