The actual difference
A mechanical machine selects stitches, length and width with dials that move cams and levers. A computerized machine uses a stepper motor and a board to position the needle and feed, so you get a needle up/down button, speed limiter, one-touch buttonholes and a stitch memory. The motor that drives the needle and the frame that holds it are the same idea in both.
For heavy fabric
Neither wins on paper. Motor torque, presser-foot lift and feed decide thick seams. In practice, the mechanical heavy-duty tier (Janome HD3000, Singer Heavy Duty) is cheaper for the same motor, and the straight-stitch specialists (Juki TL) are mechanical because they do one thing.
For quilting
Computerized machines bring the features quilters use every hour: needle down, a speed limiter for free motion, and a wide throat on the Memory Craft class. Mechanical straight-stitch quilters bring speed. Many quilters own one of each.
Service and lifespan
Mechanical machines are cheaper to service and rarely become unrepairable. Computerized boards can be end-of-life when parts stop. Neither is fragile; the difference is what happens at year twelve.
