If your speaking of the apron that perhaps pitches up from the street level to the height of the driveway and perhaps crosses a sidewalk. Cement is the most durable if its installed correctly , The material cost is most likely less as asphalt is an oil product and we all know how the costs of this has gone up considerably in the past few years.
But asphalt also if done correctly can last a long time but local delivery costs, disposal cost, and supplies will dictate to you which would be best for your particular instance.
Thanks for the answers, but I'm still hoping for more ideas.very small budget
how bad is the apron or driveway. Knowing what you have will prompt more answers. Perhaps a photo of the area? There are lots of folks here that may be able to assist you even more with ideas.
Currently not at location
Will send photo tuesday thank you very much