Since i'm replacing the two front door speakers should I just buy another set of speakers to put in the rear of my car? Would the sound quality be improved?
of course the rear would sound better with better speakers. spend at least 70 bucks on a pair of speakers from a place like best buy and you will definitely get improved sound. depending on how far behind they are behind your head and location can affect how much you hear them though.
The high end will probably improve and depending on the speakers and mount you may get a better mid range. What will happen is you will lose a full sound that has been designed by the manufacturer. If you replace speakers the best way to get better sound is to amplify the sound with a quality amp. and a good mounting job. Don't just throw them in and expect it to sound great. There is a lot into creating a good sound from a speaker.
Always remember the best sound is the one you like. Sometimes just adding a powered-sub can make the difference.