Similarities in setting: They are both set in the past. And, that's about it. To contrast, Red Chief is set in an old western location and time-frame, mostly in the desert and in a cave, where three males make camp for a few days. In The Last Leaf, it is in a highly civilized city, in an artist's studio that belongs to two women. There are more differences in setting than similarities.
As for ironic events, they both have endings that are rather unusual for the situation; in "The Last Leaf" it is that Behrman turned out to be an unlikely hero, tragically sacrificing his life to help Johnsy. You do not expect that the gruff Behrman, who mocked Johnsy's silly notion about the leaf, would take such pains to validate her fantasy by painting a leaf on. The ending of Red Chief is ironic in that the ransomers pay to get rid of their troublesome charge; usually, the ransomers walk away with the cash, not the other way around. So there are a couple instances of irony in the stories. To contrast the ironic moments in the stories, Red Chief is a lot more predictable as the ransomers slowly, throughout the course of the story, lower the ransom price. So, having to pay to get rid of him isn't as big of a surprise as the ending to "The Last Leaf". There isn't much foreshadowing on that ending, and it is definitely more tragic too, and less comical.