My character has severe insomnia that makes it almost impossible to sleep while jacked into her pod, or in any environment that doesn't meet her near obsessive compulsive standards. It isn't about a certain style of quarters, but more about how she cannot feel comfortable sleeping in an area she has not personally customized to her taste. Thus, she has installed sleeping quarters in just about every single ship she owns, just in case she finds she'll have to spend the night far from home.
Katrina is also a strange one, with a taste for variety and the exotic. Capsuleer life has given her a lust for new experiences, a complete 180 degree shift from her lifestyle as a State bred tube child. As such, each ship has a different aesthetic style of quarters, sometimes by virtue of being larger versions of favorite design styles. She prefers to remind herself what sort of ship she is sleeping in. The quarters on her Rokh are styled in traditional Achuran design philosophy, while those on her Bantam amount to little more than a couch and table with a fold up cot in the wall.
If it's a Gallente ship, it uses Gallentean design philosopy. Same for Amarr or Minmatar, or faction, and even pirate vessels. By far the most exotic place she has installed would be the quarters aboard her Zephyr. Eccentric, just like the ship's creator, the curved walls of the room are almost completely transparent and unbroken, save for the structural supports, giving the illusion that the room is exposed to the vacuum of space.
Like I said, it's not about how it looks, but if Katrina has had a chance to place her personal 'touch' to the style. A room that wasn't designed by her, customized by her, or furnished by her... is not hers. Thus, she cannot sleep in it.