In general, what would be the order of developing a product? Is there any suggestion that we do the competitive analysis first or comparative first? or at the same time if needed? And what are the pros and cons?
Ideally you would probably end up doing both as part of your research, so assuming you do them at around the same time it will not really make too much different the order that you carry them out.
The reason for this is because theoretically you are looking for related but similar information from the results of your comparative and competitive analysis. The comparative analysis is about trying to find similarities and differences in products and services of similar features (regardless of industry or product type), while the competitive analysis is more focused on competitors in the same market. Ultimately it will help you determine what are the unique selling proposition for your product and/or service, so it makes sense for you to be as thorough and comprehensive as you can (hence you tend to do both).
I would say that from a business stakeholder's point of view the competitor analysis is seen as more important (higher priority) and therefore this may often be done first by the business analyst. From a UX designer's perspective it may be more important to do the comparative analysis to get a better idea of the types of experiences and help you come up with some insights for designing the product/service.
However, as I mentioned previously, both are important to do as part of your research, and as long as they are carried out at around the same time and also at a sensible stage of the project, I don't think there is too much difference which one you do first.