Does the street have a curb? You'll probably need a permit to join the street - probably should call the permitting department and find out what the requirements are on that. My rental just has a dirt driveway. Is the existing driveway functional or is it all cracked up and deterioated? Even if it doesn't have the same finish slab to slab, I'd leave it alone if it was still structurally sound just to save the money. Its doubtful you will get more rent for the driveway and it doesn't do much in regards to maintenance expenses, if anything.
But to answer the question you asked: Concrete all the way. Asphalt is glorified dirt in my opinion (insofar as being used in slow traffic areas). It will not have near the life that concrete will have. I also wouldn't bother with the strips as I personally don't like that kind of driveway. There are better ways to make a "green" driveway. The problem with "green" pavement is that is main function is to allow moisture to drain into the subgrade. Saturation of subgrade soils is the number one enemey of all pavements. Ironically, a lot of architects like to design green pavement sections and then the engineers make them put plastic underneath...