At my annual Back to the Lounge party I am going to have a PvP event using my RPG Heroes By Trade. Now tabletop RPGs are generally not known for being any good for PvP - most of the time the fight ends with the first person to take an action winning immediately. There are a few reasons for this. First off is the problem that RPGs normally make characters and monsters on entirely different templates. The design principle seems to generally go along the lines of making all the character mechanics first and then build monsters that work with those mechanics. That leads to amusing situations where characters hit for 40 damage and have 30 HP while monsters hit for 10 damage and have 200 HP. These situations make for comedic battles when monsters fight each other and can't do anything while the players one shot one another.
The second problem is the tendency of games to hand out powers that are on a daily limit. When you have to survive multiple encounters in a day players naturally are conservative with their use but when facing down an equally powerful group in an arena it makes complete sense to go nova immediately. This generally means that ridiculously overpowered abilities all come out on round one and whoever lands one first ends the fight; just imagine how silly a 2nd edition DnD pvp battle turns out. The wizard casts sleep. The entire enemy party falls unconscious. Good fight!
Thankfully I think HBT will actually work out pretty decently as far as PvP goes. I built monsters along the same lines as characters by making sure that their defenses, attack bonuses, armour values, and such all are in the same ranges. Monsters also get abilities that are very similar to character abilities both in mechanics and in overall power level. The main thing that some monsters have is enormous HP totals. This was necessary so that building a fight against a single enemy would be feasible - plus, it does make sense that a 15 foot tall giant takes a LOT more punishment to take down than a human.
The advantage to building monsters this way is that characters fighting each other should work out well. They will be attacking into the same range of defenses and HP totals as they would if they were fighting another group of random monsters. The primary difference is that their enemies will be extremely intelligent and will do things like focus firing down one target rather than just bashing randomly. Not that every fight has to be against a dumb opponent of course but the goal is to have fun and having all the monsters attack the wizard until he dies isn't much fun for the group even if the monsters do end up losing. In PvP everyone sure is going to attack the wizard and he sure is going to die, that is just how it is done.