As someone that genuinely loves both, I don't think one can replace the other as they have been both precious to me. However Yoshi's Island is a game that feels a lot better crafted, which is something you can see in the level design. I have never attempted to 100% complete DKC1 and I have done that at least three times with YI.
DKC1 is not without its faults and the internet will always remind you of it. I don't think my vote would change if YI was up against DKC2 as well, although it would be a lot closer in quality. The question between DKC and Yoshi Island as a series would have me hard pressed. I probably would choose DKC then, as I'm perfectly satisfied with just Yoshi Island, don't need a new game in that series, but I'm always craving for a DKC game especially after both Returns & Tropical Freeze didn't win me over.