The European rabbit seems to be in fact two different species. In 2026 it was proposed to split it in Iberian rabbit from West Spain and Portugal, and European rabbit from East Spain and the rest of Europe. Both were isolated in the glaciation in opposite coins of Spain and the split is supported by genetic analysis and Iberian has a darker fur. They had barely interbred since 2 million years ago.
So we know now that moving European rabbits for hunting purposes to Portugal, Malaga or Galicia may be a menace for Iberian Rabbit.
USA has the cotton tail rabbits on genus Sylvilagus that was the original carrier of Myxomathosis virus. They live in swamps and forests.
Rabbit is more "lamb" than "chicken" but none of both. It does not have a strong flavor really. Is a common dish in the Mediterranean and is tasty. Its main problems are the splinter bones that can damage a tooth, and its unappealing look in the butcher shop.
Guinea pig should be similar. More fatty maybe. Very popular in South America, but I never ate those.