I've done 2 thru hikes and started both solo.
Along the AT it seemed I was never very much alone. And often hiked with someone.
The PCT however, as I got toward the rear of the "pack" I got very much alone. Even most the trip in general, I very rarely walked with in site of anyone.
Northern OR and southern Wash. I would go days without seeing another person. It was fabulous. Never more then about 3 days, but several of them. So between resupply I was only running into 2 to 4 hikers. I'd chat for 10 mins and never see them again. It's a great experience. The only other life adventure I have similar would be drifting alone on a sailboat, equally as rewarding.
Things that worried me? Stupid wild cat warnings. Posters around crater lake saying " Cat spoted! Don't hike alone, don't hike at dusk" Well I didnt have much choice, but it sure gives you the willies.
At the very end of my PCT hike, i ran into a few hikers and saw them on and off at least once a day. The weather was closing in and it was nice to know someone knew you were out there.
I look forward to a CDT hike, and have yet to decide if I will go it alone or with company. I am torn.