There is a major difference in the mid bass if the doors are damped correctly. I would say at least 20-30% more mid bass is achieved with proper sound deadening and also means your speakers can handle a bit more power before topping out. It can be a bit pricey but its worth it if you want a good sound. The key to a good damping is the proper sealing of the doors to prevent any air leakages and minimize the door skin flexing. Door sheet flexing results in reduced mid bass.
For the rear rattles, you yourself should also know where the rattles are coming from and direct the installer to the problem areas and they can correctly address the issue.
And if you are going to upgrade the doors, do ensure that your speakers are in MDF spacers and not chipboard. Also the spacers should be tight and NO air leakages should be there between the spacer, speaker and car door frame.