its not about whats faster its about whats better suited for a certain situation. for a long time analog was the only way to send tv signals. until the technology surfaced that could encode, compress, transmit, receive, decompress, decode the video/audio stream, analog was about the only way to send audio and/or video. digital is starting to steal a lot of the analog bandwidth (us a to d tv conversions for example) because you can use compression to get more out of digital that you could do with analog.
computers have always been about precision, which is why analog and decimal computers went the way of the dinosaur. digital was just so much faster and easier to deal with from an engineering standpoint. and the digital components got faster while analog was eft mostly abandoned in terms of development. it also made it easier to deal with digital signaling.