Almost in any situation you should prefere to EXPORT WITH IDs. There is nothing you can lost with this.
You should prefere to IMPORT WIDTH IDs when you want to maintain two copies of the same environment (DEV, TEST, ...).
You has to IMPORT WIDHOUT IDs when you import objects in an environment that has not been in that environment before, nor in a copy of this environment. For example, when you import objects from another company or created by another developer. This usually has to be done in development environment and then export-import WITH IDs to the next apps (TEST, PRODUCTION, ...)
When you import objects WITHOUT IDs, the system will assign new IDs to the objects for this application, so you won't be abble to export-import WITH IDs to another copies of the app. This will lead to problems soon or late so it should be avoided.
There are exceptions to this rule but to be sure of picking the right option in any situation you have to understand well this best practices.