I can't compare the two - I took the Norte and switched to the Primitivo though. I liked the Norte (before switching to Oviedo/Primitivo). Beach areas were gorgeous. But there was a lot of time spent walking through bigger cities and touristy areas. For me - it had more of a "hiking city to city" feel as opposed to hiking a pilgrimage. I definitely enjoyed the Primitivo more overall.
The Primitivo is definitely more "pilgrimage" like, and while I saw many more "pilgrims", it wasn't hiking city to city which made it much more pleasant.
Primitivo had easier to spot pilgrims, but I could still easily walk alone when I wanted to. On the Norte - if you weren't walking with pilgrims then you didn't easily spot pilgrims as you passed through towns. On the Primitivo - you could see pilgrims getting together at bars along the way and in towns. It really is the perfect balance of being with other pilgrims if you want to, but you are easily able to be alone when you want to. And the Primitivo had WAY LESS car traffic. You often hike in more remote areas and towns are further apart. It is wonderful. More albergues on the Primitivo, less "touristy" accommodation. Not a lot of bars/restaurants in between towns, but it was somewhat that way on the Norte too. I just always carried snacks (on the Norte and Primitivo), and waited until I got to town for lunch most days. I also carried about the same amount of water on both trails. The number of services I felt was still adequate for both.
I walked late May (Starting in Hendaye) - late June. Weather was pretty comfortable, I only had 4 days that I thought it was "too warm" - but of course - the big heat wave started just after I arrived in Santiago.
Again - my comparison is the first half of the Norte and the Primitivo - I haven't walked the 2nd half of the Norte.