I can't decide which out would be the bigger insomniac out of Annie and Armin. Annie probably adores sleep and I do think she prefers sleeping in late (Armin's the early bird) but I can't decide which one actually falls asleep.
I think it might depend on the night, really, and how busy their brains (and days) are. If they're over thinking, of course they can't sleep, but Armin buries himself in his commander duties and forgets to sleep and Annie's terrified she won't wake up for another 4 years if she goes to sleep.
So do they both lie awake in silence staring at the ceiling until the sky is bright (unless Armin is working)? (they probably pretend to be asleep so the other one wouldn't notice and worry even thought they both know the other is awake)
ORRRR is one asleep and the other awake and grumpy over the fact they're gonna be groggy and tired all day tomorrow?
I'm interested to see your thoughts on this
Who falls asleep huh? Okay, so we're talking about a post canon time period after some years have passed.
Armin does strike me as someone who has very unhealthy sleeping habits, often staying up late into the wee hours on work and fine print. This can get to the point where he's driving himself to near-collapse and someone has to step in and drag him to bed. In such states, I think it's reasonable to say that as soon as his head hits the pillow, he's out cold.
On the other hand, if it's one of "those" nights when Armin's feeling very bad about himself, then sleep doesn't come well. He either spends the night tossing and turning in bed, or decides to put his mind to work on some papers. But let's say he's got a season off work and is more relaxed, then he probably sleeps well.
I have this personal headcanon that in a general, overarching sense, both Armin and Annie sleep really well with each other because of the feeling of comfort and safety each other provides.
As for Annie, now. If I'm not wrong, she wasn't asleep for all of those four years in the crystal. It was more like a state of constant paralysed wakefulness. Perhaps if she fears anything, it would be being unable to move and feel her senses, imo. So good sleep is something she really hasn't had for a long time. She'd actively crave it. That said, I think it's more likely for her to be the one who's more of an insomniac in the normal sense of the word, because she's spent so long not sleeping that she finds it hard to fall asleep now. Still, as time wears on, it becomes easier, especially once adapted to the certainty of Armin's presence next to her in bed.
Then there could be situations where both of them are relaxed and calm, but they stay up all night talking (well, Armin talks, Annie listens). Then let's say they've had a fight, in which case both of them are awake and unable to sleep because The Sad™ is too much, and both are left wondering if the other doesn't like them anymore and if they'll be left alone (dramatic, but hey that's how they are).
They could also be suffering from nightmares from the past, which would give both a reason to avoid sleep.
So as you say, it depends on the time period (years post rumbling), the states of their minds, their relationship and so on xD