This seems to be an interesting and ambiguous topic.
On one hand, the collagen as any other protein is cleaved into small-sized chunks (oligopeptides) and single aminoacids before absorption. The chunks of proteins which were not completely digested before absorption are broken up further in the body and cannot be selectively used for collagen re-building in the body. Therefore, there should be no difference between the collagen of different types and, basically, no difference between the supplements containing collagen and just a mixture of aminoacids. This also explains the fact why collagen supplement is in most cases taken in the lysate (pre-cleaved) form.
On the other hand, a quick search in PubMed and I found an interesting article on the topic (source), where the authors claim:
At 6 months, the proportion of clinical responders to the treatment,
according to VAS scores, was significantly higher in the collagen
hydrolysate (CH) group 51.6%, compared to the placebo group 36.5%
This study suggests that collagen hydrolysate 1200 mg/day could
increase the number of clinical responders (i.e. improvement of at
least 20% on the VAS) compared to placebo. More studies are needed to
confirm the clinical interest of this food supplement.
So, if the article is not a bogus (I failed to get the full version of it and the journal does not seem to belong to the top journal in the field of medicine), there could be some mechanisms yet to be discovered.