There might be a slight difference in the meaning. If you say
Die zwei Kulturen prallten aufeinander.
then you don't make any more statements than that there is a clash of cultures, whereas
Kultur X prallte auf Kultur Y
might have two additional connotations
Y is the predominant culture and a smaller group X might collide with it
that X is somehow responsible for the clash of cultures, for example by deliberately provoking it.
These additional connotations are not necessarily always present, it may depend on the context of the sentence.
Other situation where you could use "aufeinanderprallen" is "Meinungen" or "Ansichten", but I would not use for "Ideen" or "Vorschläge".
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To be honest, I would not use "aufeinanderprallen" for "Vorschläge", but "kollidieren"
Mein Vorschlag kollidiert mit der traditionelle Vorgehensweise.
(please be aware that this is a pretty strong statement, that suggests that your suggestions is not possible because of the traditional way of doing.)
Another possibility would be "treffen:
Mein Vorschlag trifft auf die traditionelle Vorgehensweise
This would also work for "Ideen":
Meine Idee trifft auf die traditionelle Vorgehensweise