1) The basses are not identical so the sound will not be 100% identical. That being said, if the basses are identical in every way, except that one has 4 strings and the other has 5 strings, they should sound pretty close.
2) If you are looking for a "flat" frequency response, then definitely you will want a mic that can capture the extended frequency response of the 5 strings. However, most engineers do not record the bass "flat." See our Recording sub forum for some good advice how to record your bass (or just hire a pro engineer for your first recording so you get an idea how it works).