I had a bunch of people over to play board games this weekend. Even though the group as a whole really likes to play board games we had a hard time agreeing on a game to play because anything there was a lot of interest in got vetoed by somebody or other. The problem seemed to revolve around how much PvP there was in the game and how critical moments of PvP resolved themselves. For example, in Settlers of Catan you have lots of small PvP moments where you have to place the robber baron on somebody's land or decide which player you will trade with when you have identical offers. These choices do matter but the stakes are low and they certainly don't make and break games on their own. There are also critical PvP moments where one player builds several road segments at once and drops a settlement in a location that somebody else was all set up to take. When this happens it often is such a blow that the player getting ganked is pretty nearly out of the game.
We ended up playing Vegas Showdown and got to see exactly why it has this same sort of issue. There are plenty of times when you are faced with the choice of two relatively equal options with the only difference being 'who do I want to punish?' The trouble is that often the game ends up revolving around somebody buying the Theatre and then struggling to place it - it is common that if they do place the Theatre they win and if they don't they lose so there is a very high stakes fight over it. This isn't a problem in a two player game so much but it becomes pretty annoying in a five player game because people end up arguing over who has to bite the bullet to block the Theatre player. Puerto Rico is similar because again you have lots of small options to hurt somebody and then in the endgame you can easily hand someone 10 points by calling Craftsman in just the right (wrong?) place and playing kingmaker.
Factory Manager ends up being entirely the opposite but in many ways just as problematic. In that game a good player will make few or no significant mistakes over the course of the game and gaining ground early has a snowball effect so if you get stuffed (or do something stupid) in the first turn you are often out of the game. There just aren't enough critical points for you to find a way to get back into the game in most cases so the person who is ahead on turn two will usually cruise to victory. I think both of my games, FMB and Dot, fall more into this category. There are a ton of small decisions to be made throughout the game that matter a lot but there is rarely a big 'well, now you lose' moment unless the game is incredibly tight. Sometimes I get feedback from testers that the games don't seem to have any big changes and you just keep playing until somebody wins; this is true and it is all part of the package. If there are critical moments then it allows for a weaker player or a player who is behind to catch up and that isn't my design goal.
I don't see a good way to design a game to get out of this trap. If you have big critical PvP moments then people will end up fighting over what to do and some people will really dislike that. If you don't have those moments then anyone who falls behind a little has no chance to get back into the game and some people will really dislike that! Hell, you will find some people who dislike both, in which case it will be hard to find a game they like to play consistently. Either way I seem to end up designing games with very few critical PvP moments that are won by an aggregation of small decisions; that probably accurately reflects the sorts of games I like to play.