Either one is bad. Actually, rotational play causes fewer problems, but the sort of slack I think you are describing lets the driv - err propshaft fall to the side, off center. Where it vibrates, giving you the more noticeable symptom of a U-joint dying.

Ahh, I used to trash so many U-joints in my old 122. It had the tiny ones, and the scary u-bolt yokes. I was in high school, and abused the poor old car mercilessly. Limped it home a time or two with a u-joint held together with bent coat hangers. Eventually I swapped in a beefy big u-joint 142E driveshaft (and the engine, trans, and rear axle too for good measure) and never broke a u-joint again...
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I'm JohnMc, and I approved this message.