Personally, I have a great desire to maximize my DPS in Expert and 60 roulette, and try as hard as I can. I get really mad at myself if I mess anything up or miss a timer.

That said, I don't care strongly about trying in Trial or 50 roulette. I do them, I try enough needed to win, but meh.

The weird one for me is Void Ark. In some ways, I find it more fun to mess up. I don't actively try to mess up, but I goof around a lot in there. It's just brain numbingly boring otherwise. I usually goof around by throwing out random stuff in alliance chat "What happens to a bunch of catgirls that take up battle against a Tentacle beast?" etc. Though that often results in me focusing less on maximizing my potential.

I think it comes down to three aspects:
1. Difficulty of Content
2. Composition of party members (are they a static, fc mates or strangers etc)
3. Number of players present

I am going to elaborate more on each now.

Difficulty of Content
When content is tuned ridiculously easy, I (and I am sure many others) do not care to try very hard. It's easy content, so we faceroll through it. As we do this over and over, the content becomes excessively boring. It's at this point we entertain ourselves in a number of ways that all detract from our potential. This could be things like watching netflix, goofing around, jumping in circles, chatting to your FC and so on. With my example above, Void Ark is in a weird spot. It was very easy for a raid, I cleared it without problem on my first run and with having 0 idea what any of the mechanics were. In fact, I didn't know some of the mechanics until my 5th time in, but despite this, it was easy to clear and I didn't die or anything. That said, it's hard enough that there are mechanics, and the more people who goof off, the more difficult the content becomes.

Composition of party members
I am not sure about all of you, but I try the hardest when I am with my static. I want to be at my top game for them, as I want them to be at their top game for me. This is where I really try.

My second best set of people to play with is usually randoms. In this case, I don't want to be the person wasting peoples time, so I do what I can to get us through the best.

My third best set of people to play with are usually friends. I care about these people and don't want to waste their time, but I know that they'll forgive me for mixups and I'll forgive them. It's more light-hearted.

My worst set of people to play with are usually FC mates. These are people that I care about, but probably less so than friends or static-mates. They're close enough that the run is light-hearted, but not close enough that I don't care if I mess up. These runs actually tend to be the worst for me. FC party runs of Void Ark are the absolute worst. To clarify on this, I find that everyone in the party acts this way, not just myself.

Number of Players Present
This is just a factor of how much impact you have on an encounter. When there are 24 people there, your impact is much less than when there are 4 people. In a dungeon run, I can expect to do about 50% of the DPS of the run on my SMN (on average), whereas on a Void Ark run I can expect it to be closer to 9-10%. So when I miss my deathflare in a 4-person party, it makes a pretty substantial difference. When I miss it in Void Ark, meh.