The 0.60mm gives more high harmonics, the 1mm gives less, the .073mm is in-between. Depending if you want more of a lead sound or a rhythm sound. The 1mm is great for fat metal tones, the 0.60mm is neat for playing without the amp (I know it's a sin), the extra harmonics let you hear yourself better.
But the 0.73 does everything well, when in doubt use that thickness. I had only the 0.60 stuck between three guitar strings, but now I also slide a 0.73 on the other three strings. Easiest way to change the tone without touching the knobs.
Next time I will also order triangular 0.73's for my bass. I don't know a more rigid and more glassy material than Ultex for picks. I have one in my pocket all the time together with coins, never seems to wear out or get scratched. It does lose elasticity after a couple months, like all the others, that's why we buy them in packs.