If you'll indulge me in using Wikipedia as a
reference, what I found is that the original Apollo Guidance Computer (AGC) had hardware comprising approximately 5600 "gates" (each gate equivalent to a handful of transistors, compared to a modern CPU chip containing
millions of transistors; was clocked at a little over 2 megahertz, compared to several
gigahertz for today's CPUs; had less than 64K bytes total memory (ROM plus RAM), compared to on the order of a
gigabyte of RAM today; used a calculator-style pushbutton pad for input, with output for the astronauts via an array of 7-segment numerals; and had no disk drives. The hardware was connected using wire wrap (no soldered printed circuit board) and then cast in epoxy.
Software was equally primitive by today's standards.
As for cell phones, I don't know the exact hardware specifications but I'm sure it's closer to your desktop PC than to that AGC!