Is there a greater fundamental difference between plants and animals or between prokaryotes and eukaryotes?
An interesting question! To be honest, this is like comparing apples and oranges, or maybe apples and puppies. Both plant/animal distinctions and prokaryotes/ eukaryotes distinctions are major, and understanding both are essential for understanding biology. However, if I had to choose, I'd say the prokaryotes/ eukaryotes difference is larger. I have two general reasons for this. First, the distinction between bound cells that can live independently and cells that only survive as tissue is huge. Second, evolutionarily this split is earlier. (Plants and animals came from the prokaryotes/ eukaryotes split, and so are derivative.)