I'm not sure what GM meant by radial tuned (the big-3 were famous for hype) but for most that meant stiffer front suspension, different shock ratios, and (sometimes) changed front suspension geometry. Basically, done properly, you got less understeer from that 800 lbs hanging on the front axle.
Early Michelin radials were built for long life, not great traction in high powered cars. They were narrow and did great in snow, but affected handling on many makes. Hang a set on a VW bus or beetle and they'd last almost as long as the engine, but made cornering a bit more tricky, as the VW was designed for some rear slip to keep the axles from lifting. It's one of the reasons VW switched from swing axles. Dad put a pair of fatter bias tires on the VW van, but made the mistake of putting them on the back. I quickly moved them forward, where they belonged... skinny originals on the back.