Yes, it's roughly similar. What happened to american and european Spanish, american and european English, american and european Portuguese is roughly similar indeed.
The differences are mainly in the spoken languages, but I'll list some to you:
Spelling:
European Portuguese uses a more primitive spelling, many times just for marking etymology (mute, therefore). When brazilians use the primitive spellings, they pronounce all the letters and usually atribute a different main sense.
Also, since Brazilian Portuguese prefers cult adjectives for non-vulgar word constructions, 'modern' nouns may direct you to primitive spelled or quasi-latin adjectives.
European Portuguese prefers to fully adapt Greek (and even Latin) words for the distinctive Portuguese ortography, whereas Brazilian Portuguese would allow you to choose, being the closer to the original possibly more common.
Úmido (br.) - Húmido (pt.)
Ação (br.) - Acção (pt.)
Ótimo (br.) - Óptimo (pt.)
Suntuoso (br.) - Sumptuoso (pt.)
Próton (br.) - Protão (pt.)
Cálix, Cálice (br.) - Cálice (pt.)
Fato (br., noun) - Factual (br., adjective)
Facto (pt., noun) - Factual (pt., adjective)
Trema:
This diacritic mark is used in Brazil but not in Portugal. However, the pronunciation is the same.
Freqüente (br.) - Frequente (pt.)
Bilíngüe (br.) - Bilíngue (pt.)
Acute Accent:
European Portuguese don't use the accent in some places where brazilians would.
Idéia (br.) - Ideia (pt.)
Alcatéia (br.) - Alcateia (pt.)
Grave Accent (Crasis mark):
Brazilian Portuguese may prefer to do not use the accent where European Portuguese would.
Pra (or prá, prà; br.) - Prà (pt.)
Cincunflex Accent:
European Portuguese commonly uses the acute accent where the brazilians would use the circunflex accent. This generally represents pronunciation differences (pt: open, br: closed).
Sinônimo (br.) - Sinónimo (pt.)
Cômodo (br.) - Cómodo (pt.)
but
Três (br.) - Três (pt.)
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