I believe we have a subtle difference between these adjectives.
Crowded describes the state where there are a lot of people in the same place (a crowd), but they are not necessarily extremely close together - for instance you can have a very large crowd in a busy market, or a town centre on Christmas Eve, or a popular football match, or a pop-concert. You can have a crowd of 100,000 but there is still room for everyone to move around. In Sociology, crowded is a temporary gathering of people responding to common stimuli and engaged in any of various forms of collective behavior.
Ex.: The bus was crowded.
(1) O ônibus estava lotado.
(2) O ônibus estava tumultuado. = [tava uma bagunça só.]
= O ônibus estava abarrotado de gente. [Brazilian regional term]
Packed means very close together so that one can't move relative to another. It doesn't necessarily have to be crowded to be packed - for instance, a bus could be packed because there might be 50 people standing on the lower deck it when there was only room for 30. That isn't a crowd, it is packed!
- [lotado, cheio].
Ex.: The train was packed. = O trem estava lotado.
to be packed with/packed full of
(estar cheio de, ter muitos/muitas)
Ex.: The guide is packed with useful information. = O guia tem muitas informações úteis.
REFERENCE: Pearson Education. Longman Dictionary. 2004.