Computerized has electronics inside: chips, boards, etc. Mechanical has gears. In my humble opinion, mechanical has an advantage because it's much easier for the owner to perform some basic troubleshooting and servicing of the machine.
My Brother 1500 is mechanical and has a needle threader, thread cutter, needle up/down, and a knee lift. I also have a service manual and when something's not working right, I hand it to my 22 year old son and he makes my machine purr again.