It depends on the car and the tread design of the tire. It has nothing to do with radial or bias ply tires. Some of the new tires are rotation specific, meaning they cannot be swapped from one side of the car to another. Front wheel drive cars do all of the work and those tires wear much faster than the rear, so swaping front to rear makes sense (moving from the front left to the front right would result in one tire going bald soon). When you rotate a rear wheel drive car tire from one side to another, the tread wear will increase until the tire gets used to riding backwards.
There is ample evidence, as noted in your owners manual, that rotating front to back on the same side, is the best solution. And if you rotate at least every other oil change, your tires will wear evenly.

Klaus
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1975 164 w/174,800mi (Sold) 1995 850T w/91,000mi, 1998 V70R w/129,000mi