Yonks,
Here's my equation on the subject from about two years ago:
Rubber cleated hip boots + slippery mountain stream in Virginia = finishing off old football injured right knee + three months off work (luckily on short term disability) + some rehab + missing about a whole best part of the season (March to June)
Felt soled chest waders = hardly any slipping
And, I always carry and use a wading staff now