The memory model is similar (a flat, linear address space). The OS APIs are quite different. Fuchsia's OS APIs are designed around an object-capability discipline. For example, almost all the syscalls take a zx_handle_t as their first argument, which means they are operations on an object the process has previously been granted access explicitly. In Linux, many OS APIs operate on the "ambient" environment rather than on a specific kernel object.
Disclosure: I work on Fuchsia.