Linux is both older than Symbian and wasn't designed from scratch since it's derived from Unix. So I guess it's a philosophical question whether Android is Linux or something new.
Linux is just a kernel, and only a Unix-like kernel at that. It is not an operating system. You're probably thinking of the GNU/Linux operating system, but then GNU is a recursive acronym for GNU's Not Unix. Android forgoes the GNU part, but maintains the Linux part (albeit with some patches).
While both written from scratch at some point in history, the trouble is that Linux is the newer one. Symbian is rebranded EPOC, which is older than Linux.