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Desarrumado vs. bagunçado

While both desarrumado and bagunçado refer to a state of disorder, the main difference lies in regional preference and intensity. Desarrumado is the standard term in Portugal and implies things are simply out of place (literally un-arranged). Bagunçado is the most common term in Brazil to describe a mess or chaos, but it is rarely used in Portugal.

Desarrumado

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This word comes from the verb meaning to tidy or to arrange. It is the primary word used in Portugal to describe an untidy room or appearance. In Brazil, desarrumado is also used, but it generally refers specifically to things being out of their designated places, whereas bagunçado implies a more general state of chaos.
O teu quarto está muito desarrumado.
(Your bedroom is very untidy.)
Não gosto de ver a casa desarrumada.
(I don't like seeing the house untidy.)
Ele apareceu na reunião com o cabelo desarrumado.
(He showed up to the meeting with messy hair.)
Deixaste o escritório todo desarrumado ontem.
(You left the office all untidy yesterday.)
As roupas ficaram desarrumadas dentro da mala.
(The clothes became disordered inside the suitcase.)

Bagunçado

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Derived from the noun for mess or ruckus. Bagunçado is the everyday word for messy in Brazil, covering everything from a cluttered room to a chaotic schedule. In Portugal, this word is predominantly understood but seldom used; Portuguese speakers prefer desarrumado for physical spaces and verbs like confuso for abstract situations.
A sala está toda bagunçada depois da festa.
(The living room is all messed up after the party.)
A minha vida está um pouco bagunçada agora.
(My life is a bit messy right now.)
Estes arquivos estão completamente bagunçados.
(These files are completely messed up.)
O trânsito na cidade está muito bagunçado.
(The traffic in the city is very chaotic.)
Não deixes o teu guarda-roupa bagunçado.
(Don't leave your wardrobe messy.)

Summary

In short, if you are in Portugal, use desarrumado for almost all situations regarding untidiness. If you are in Brazil, you can use desarrumado for things out of place, but bagunçado is the more natural and common choice for general messes.