I have walked the Spanish part of the CP and all of the CF. They are pretty different to me. When I walked the CP, it wasn't June/July/August, when I am sure it is busier, but to me it was very quiet. I would run into very few other pilgrims each day. There seemed to be a lot of cylcists from European countries. The scenery is also quite different, being close to the coast. I found that a lot of the path was really close to the coast, but not quite on it, so now and then I deviated to the coastline and came off the camino, just to get near the water. I don't know what the Portugese part is like. The coast line is definitely very pretty.
I personally found that there have been more friendships made on CF, more conversations had, more excellent pilgrim menus, and so many varied, tiny, quaint towns. It also has the whole spiritual significance that makes it seem more special in some ways...but if you want more quite, solitude, then definitely the CP. CF, I am sure, will be fairly busy in June and this may mean having some competition getting beds at albergues, etc, I would expect...