The phonology of European Portuguese and Brazilian Portuguese
There is some weird stuff going on with these two variants that I think it's interesting to explore because they diverge in more than just vocabulary, as the phonology for each one moved in different directions — and in the European Portuguese case, removed itself quite a bit from the usual path Romance languages have been following.
I should note that I won't cover African variants because (a) Portuguese-speaking African countries follow the European Portuguese rules already and (b) each country can also have its own linguistic traits I'm not familiar with. That's the same reason why I won't touch the variations spoken in Macau, East Timor, and possibly Goa.
So, the first thing to note is that Brazilian Portuguese was heavily influenced by African and, especially, Indigenous languages. Toponyms like São Paulo, Rio de Janeiro, and Salvador are very Portuguese names, but then there are things like Ibirapuera, Itabira, Tocantins, Pindamonhangaba, which are indigenous words. Sometimes things get mixed and sound quite funny, like Pirapora do Bom Jesus.
That's not a surprise, considering that the Tupi, an indigenous language family, was widely spoken country-wide in the later colonial times, in the 17th and 18th centuries, mixed with a bit of Portuguese. The most common variants seemed to be the Língua Geral Paulista — which completely disappeared, but influenced the Caipira accent spoken in the countryside nowadays — and the Língua Geral Amazônica — or Nheengatu, still spoken by some people in the Northern region, but in diminishing numbers.
I'm saying this because these languages make heavy usage of vowels, and a phonological characteristic of Romance languages is also the insertion of vowels after a consonant when that consonant doesn't already have a vowel. In Brazilian Portuguese, the most common example is the word "pneu" ("tire", the thing cars have on their wheels), which is pronounced as "peneu" or "pineu" (emphasis to show the addition of a vowel when speaking). This is called epenthesis.
That doesn't happen in European Portuguese, where most unstressed vowels are suppressed or reduced. Portuguese usually speak keeping the same "distance" between the stressed syllable on each word in the sentence, keeping a somewhat "steady" rhythm. People sometimes even confuse it with Slavic or Germanic languages, when hearing it for the first time, because it sounds like just a lot of consonants together without vowels in between.
In Brazilian Portuguese, on the other hand, each syllable keeps its own space, even with unstressed vowels. Given the size of the country, some regional accents do suppress some syllables in some situations, but as a rule of thumb, if you pronounce every syllable, it's alright.
In short, European Portuguese is stress-timed, a trait that is associated with Germanic languages, while Brazilian Portuguese is syllable-timed, a common characteristic among Romance languages.
[A personal note here, but I find it easier to understand Portuguese-speaking Africans than Portuguese people, and it's probably due to this.]
Now, why is there such a difference? I have no idea. Some people say the European variant's phonology is influenced by Celtic languages, but I really never dove into the topic. The Brazilian variant keeping its vowels makes sense, considering the indigenous language influence, but that would still make the European Portuguese the exception in the Romance language tree.
There's one theory, though, stating that modern Brazilian Portuguese kept the European Portuguese phonology from the Age of Exploration, while European Portuguese actually changed in this regard in the last few centuries. Why do some people think so? Because the Portuguese epic "Os Lusíadas", narrating the Portuguese, ahem, "exploration", in heroic decasyllable verses in ottava rima, keeps its metering better when read with a Brazilian accent than with a Portuguese one.
Of course, this is just a theory, I'm not knowledgeable enough to say if there's some credibility or not to it, just like the Celtic influence one. But it is funny that European Portuguese went the opposite direction from other Romance languages, especially considering that modern Galician, a sister language (Galician and Portuguese both branched out of the Galician-Portuguese) has a prosody closer to Brazilian Portuguese than European Portuguese.
[Another personal note: I understand spoken Galician better than spoken European Portuguese, and I never studied Galician.]
There are many records about phonemes changing over the centuries, or studies about stressed syllables, but apparently nothing about isochrony in a historical context. And I'm here like "nobody thinks this is weird/interesting?" lol
So yeah, that's apparently another linguistic mystery.
[Side note: It's worth mentioning, that both variants have the same grammar, even if they diverge in orthography and some other regional traits.]