You are not comparing pvp and pve. You compare multiplayer vs singleplayer. Both pvp and pve are multiplayer.
All three have their audience. If you are single developer, multiplayer is hard. Especially real time multiplayer. And there is the question, if it is mandatory multiplayer or optional. Is the core game a multiplayer experience, or is it just something that could be shared by several people playing together. Or is the game fun only there, because you can play against other players.
In games, pvp is very popular. It's just, that pvp is so often seen in real world. Be it chess or any sports.
I am hard pressed to find real world examples of pve. I believe those evolved from the fact that in computers and board games, you have to face the problem of a sore loser - and of grievous play. And pve is somewhat easier to implement in a computer game, than in a sports event. So they are there, because it is possible. You now only face the problem, if the pve game should be playable by one person or if multiple persons are mandatory.
It is a complex question and there is no straight answer. I depends too much on the type of game. And of your capabilities to actually implement any such game.