For me there is a distinction between "character conflict" and true PvP.
Character conflict can be a good thing. In a memorable moment of a previous campaign, two PCs came into conflict. One was a young psionic girl who didn't want to bathe (street rat, 1 level of Commoner.) The other was a young female bard (ex-noble, 1 level of Aristocrat.) They were going to meet an important NPC and the bard insisted that the little girl take a bath, while the little girl refused.
So when push came to shove, the bard said, "I grab her." At that point, we ran it as a PvP combat. It was mostly grappling, and in the end, the very agile little girl easily evaded the bard's attempts to give her a forced bath.
It was great fun. Everyone had a good time, and the combat rules worked perfectly for what one PC wanted to happen. Great.
True PvP is where one character is actively trying to kill another. I've never seen this turn out well. In one case in a game of Shadowrun, I was the culprit. We were taking a job to defend a village from assault. In the previous game, another player had argued vehemently with me to instead join the attackers for a larger fee than the villagers could pay. I refused (as did the other players) and the character and player of my opponent stormed off.
Next game, this guy's character shows up at the village. I was angry from our argument the previous session, and decide that there was no way my character--a Shadowrunner--was going to trust a guy who lobbied for joining the attackers, disappeared for a day, then comes back moments before the expected battle. There was a confrontation, which devolved into a gunfight, which ended in his character getting killed.
Unpleasant feelings all around.
Maybe it works for some folks, and more power to them. But I don't allow it in my games, and as a player it's cause to head for the door.