Answer to Question 1
An advantage of this approach is that it can uncover novel coping strategies that are not included on a checklist. However, the narrative approach, too, has its shortcomings. For example, unlike checklists that prompt one's memory about different coping strategies, narratives have no prompts and so coping strategies that are used may be forgotten. Folkman and Moskowitz (2004, p. 751) conclude, there is no gold standard for the measurement of coping. The measurement of coping is probably as much art as it is science. The art comes in selecting the approach that is most appropriate and useful to the researcher's question..
Answer to Question 2
One study (Stone et al., 1998) that compared reports of retrospective coping with those of momentary coping found that the retrospective approach under-reported cognitive coping strategies and over-reported behavioral coping strategies relative to the information collected using momentary coping data. Which then is most accurate, the retrospective or the momentary reports? That's not entirely clear since even the study's researchers noted that participants making momentary reports may also forget or omit information. For example, since the participants had to report information repeatedly, they may have thought they had already reported particular coping strategies that they in fact had not reported. Further, they may have focused on more concrete well-defined stress-related problems in their momentary reports rather than larger more abstract problems that become more apparent across longer time spans. Thus, the momentary reports may not be as sensitive a measure for collecting information on how people cope with more abstract stress-related problems as retrospective checklists.