Both critical of anachronistic appropriation of history, but differently:
Hadot: Intention of ancient philosophical models recoverable by understanding genre
Gadamer: Recovery of original intention as error of Romantic hermeneutics. An ancient author’s text is not a recoverable model but an interlocutor. If interpretation can be viewed as “re-creation,” it “is a recreation not of the creative act but of the created work, which has to be brought to representation in accord with the meaning the interpreter finds in it” (Gadamer, 1960/1990, p. 119).
Both situate historian as a historical being with a particular horizon:
“That the historian is himself an historical being, that the past can only be thought in the present, by a living being who necessarily has a particular perspective: all of this is hard to deny. That it is a matter of existential urgency to give a personal, living, formative sense to our enquiries into the past—that is what historians and philosophers of Antiquity had long taught” (Hadot, 1990/2010, p. 75)