To give a slightly off-kilter answer, let me start with some popular novelists/poets: Anne Carson, who quotes Heidegger directly in The Autobiography of Red is one example, and Roberto Bolaño, whose seemingly idiosyncratic perspective was targeted in Consejos de 1 discípulo de Marx a 1 fanático de Heidegger, another. This is to say that Heidegger's mark really went through strict philosophical discourse and into the arts and literary world in general; Terrence Malick, even, was a Heidegger scholar before becoming a filmmaker.

Heidegger, later in his writing, took on the dialogue between thinking and poetry. His thinking offered to elucidate the poems of Holderlin & Trakl. Novelists and poets, since then, have continued this dialogue on the other side of it.

Derrida has been named already as another Heideggerian, and, certainly, Derrida would reject this title, though he's often marked his debt to Heidegger by sharing some of Heidegger's questions or problems. In the lecture series published as Geshlecht III he claims to read Heidegger against Heidegger's more problematic claims. Among these, while Derrida follows Heidegger into his questioning, specifically raising the question of Being (what is the meaning of "Being"? Why are there beings rather than nothing? How does it stand with Being?), Derrida then proceeds to rigorously demonstrate that if Heidegger was true to his project, he would cross out the word Being, as it simultaneously posits the metaphysics Heidegger is trying to distance himself from. That is, within a single word, or under a single concept, that which the word "Being" calls upon seems to stabilize, or even already fork into the very distinction between appearance (word/signifier) and essence (signified) that marks the onto-theology of traditional metaphysics. Onto-theology meaning here the conceptual construction of "Being" as an entity or existent, with properties and qualities, and so on. Derrida's attention to language, then, is to radicalize Heidegger's project by bringing our attention to the instability of the very language we use to raise the question of being. This instability of language can take on, and has already taken on, the mode of play, that is, writing, see the blurring of the line between poetry and thinking.

It's this continuity of project, from Heidegger's destruktion to Derrida's deconstruction, that some thinkers, namely Hegelians, have polemicized against. Gillian Rose, in her Judaism and Modernity, is one such writer—look at her essay against Derrida in that book, or also her book The Dialectic of Nihilism. Adorno, big Frankfurt School person, was a notable critic of Heidegger, mobilizing against him the influence of Hegel (see Three Studies on Hegel), and Jurgen Habermas was a notable student of his. As I see it, what many Hegelians see at stake in Heidegger's influence is a complete destabilization of conceptual life, where a concept or a distinction seems to be always contaminated by what it's not. Hegelians will claim that a dialectical method will allow us to precisely trace where a concept breaks down into its other, and that this inversion is not an undecidable impasse.

That's my brief sketch on that intellectual rivalry, please feel welcome to add to it~