Long-term event study vs. difference-in-differences (DID) analysis I am trying to understand the differences between event studies and DiD analysis.
In particular, if I want to estimate the specific effect of an event like certification adoption, CEO appointment, or a specific technology introduction on firm performances, what is the most appropriate approach?
I have seen both papers resorting to event study as well as DiD approaches to study such events but none of them describes why they have selected an approach rather than another.

The "event study" is a methodological framework for the study of "events" in general, but seems to be used quite frequently in finance applications. Peruse the top answer here for a detailed discussion of this. In my review of the relevant literature, I often see difference-in-differences (DD) used in tandem with event study frameworks.
Similar to event studies, DD assesses the differences in outcomes between two groups (treatment/control) before and after the introduction of some "event" of interest. As a natural extension, evaluators often modify the DD model to look at the effects around the event date. For example, we might be interested in how the effects evolve by period in the pre- and/or post-treatment epoch. The effects by period (i.e., monthly, quarterly, yearly, etc.) represent time-varying treatment effects, and tell us something about how the treatment effect evolves relative to the event date.
You might be wondering why we extend the DD model in this way. I propose two very obvious reasons. First, the event study framework improves the credibility of the findings. Effects should concentrate in the post-treatment epoch. Effects that emerge before the event date cast doubt on the research design, and could be interpreted as selection bias. Imagine a scenario involving forced CEO turnover due to firms' subpar performance in previous years. Is a rebound in performance after the CEO is appointed due to CEO ability, or a natural regression toward the mean? As for the adoption of various certification standards, the same analysis applies. Firms pursuing a certification standard should not be trending differently relative to the non-adopters before the actual certification. If they were, the DD estimate will be biased. Part of your "treatment effect" is the differences in outcomes between the treated and untreated firms that were already emerging before the event.
Second, the event study modification allows us to answer more specific questions about timing effects. It's often impractical to assume the effect of a treatment is immediate—and everlasting. Is it safe to assume a technological innovation improves firm performance forever? Probably not. Maybe the effect is immediate, but wanes after a few years. Maybe a new CEO appointment does affect performance, but with a 2-year lag. Note that summarizing the "treatment effect" pre- versus post-policy with a single coefficient won't help you answer questions about timing. If you're interested in when effects emerge or their persistence, then the event study specification affords you greater flexibility. Review the top answer here for other examples of when persistence may be of substantive interest.
I cannot definitively answer the question of which methodology is the "most appropriate" without knowing the specifics of your study. I often see DD and event study methodologies used together in the same analysis. Evaluators will often seize on opportunities to investigate "events" that affect only a subset of the actual market. That group of untreated/unexposed firms is then used to estimate counterfactual outcomes, which is a state of the world in the absence of the event. This is often a more credible approach than a single event affecting a whole market.
