I guess it kind of depends upon your situation, but generally, I'd advise on carrying your own tent. There are plenty of couples that do share tents on long distance hiking trails, but as Bob eloquently stated,having your own gear makes sense, especially if you become separated.
I experienced some knee issues and hiked slower than my compatriots and had to fend for myself. I elected to do so because I knew i had all the necessary gear. Once my knee recovered, I eventually caught up to them several days later. But never were any of us beholden to the other. Obviously, if you are married or some other strong bond, that situation is different. In the case of friendship, I'd carry my own tent.
One funny story - we were hiking along the PCT and some relatives had decided to hike along with their thru-hiking cousins. These relatives decided to split gear, and at one point, one of them fell behind several hours and decided to knock off early. Well, he had packed the poles to the tent while his cousin had the tent itself. Neither seemed very pleased with the other. But the same goes with shared cooking equipment, shared water filtration and especially, shared maps.
I guess with any long-distance hike, having your own tent also provides some solace and privacy.
Have fun on your hike!