Misinformation surrounding crises poses a significant challenge for public institutions. Understanding the relative effectiveness of different types of interventions to counter misinformation, and which segments of the population are most and least receptive to them, is crucial. We conducted a preregistered online experiment involving 5228 participants from Germany, Greece, Ireland, and Poland. Participants were exposed to misinformation on climate change or COVID-19. In addition, they were pre-emptively exposed to a prebunk, warning them of commonly used misleading strategies, before encountering the misinformation, or were exposed to a debunking intervention afterwards. The source of the intervention (i.e. the European Commission) was either revealed or not. The findings show that both interventions change four variables reflecting vulnerability to misinformation in the expected direction in almost all cases, with debunks being slightly more effective than prebunks. Revealing the source of the interventions did not significantly impact their overall effectiveness. One case of undesirable effect heterogeneity was observed: debunks with revealed sources were less effective in decreasing the credibility of misinformation for people with low levels of trust in the European Union (as elicited in a post-experimental questionnaire). While our results mostly suggest that the European Commission, and possibly other public institutions, can confidently debunk and prebunk misinformation regardless of the trust level of the recipients, further evidence on this is needed.