Collective numerals

Question

Is there a preference as to when to use cardinals vs collectives when referring to groups of people with the numbers 2 and 3? I was told that collective numerals sound best with the number 2 and cardinal numbers sound best with the number 3. Thank you.

Там НЕ́ бы́ло ДВОИ́Х / ДВУХ МУЖЧИ́Н

Я помо́г ДВОИ́М / ДВУМ МУЖЧИ́НАМ по́сле рабо́ты

ТРО́Е МУЖЧИ́Н / ТРИ МУЖЧИ́НЫ сказа́ли, что они́ меня́ ви́дели в магази́не позавчера́.

Там НЕ́ бы́ло ТРОИ́Х / ТРЁХ МУЖЧИ́Н

ТРОИ́М / ТРЁМ МУЖЧИ́НАМ по́сле рабо́ты

Answer 1

If you have rather good skill in Russian language your question is fully answered in this part of the Book. And since this Book available online for free I recommend to read it whole, it will improve Russian language skill even for native speaker :)

If you don't have yet Russian language skill enough to comprehend this book here is my short translation.

Collectives differ from cardinals by shorter area of usage:

1. collectives can be used as countable for nouns used in plural form only, e.g. ворота, сутки.
2. collectives can be used with nouns дети, люди, лицо (as human being) and with nouns like ребята, волчата colloquially.
3. usage of collectives is limited by formality, cardinals are preferred in official context. Требуются на работу четыре инженера not (четверо инженеров)

Collectives are not used with:

1. feminine gender nouns or with nouns describing females, e.g. три страницы (not трое страниц), четыре сестры (not четверо сестёр).
2. masculine gender nouns that are names of animals and birds, три быка, три орла (not трое быков, трое орлов) .

It is acceptable to use collectives as variant form for cardinals with nouns having following meanings:

1. male human beings, четверо учеников и четыре ученика
2. objects that have only plural form except двое, трое, четверо, e.g. пятеро ножниц и пять ножниц
3. with personal pronouns, их было четверо, пригласили нас четверых, it is preferred to use cardinals with oblique cases, с ними четырьмя, у них четырех

Answer 2

i don't know how orthodox my opinion is, but to me collective numerals rather refer to people known from earlier or who are going to be the subject, whereas cardinals accordingly refer to people spoken of in passing who are not the focus of the statement

when i hear двоих мужчин i immediately think of two certain men i must either already know of or am going to be told about