Both plants show not so much disease as winter burn - combined effects of cold, wind and sun. The tightly curled brown leaves will not recover - the rest of the plants will. Rhododendrons are subject to many fungal infections which result in black spots. These diseases tend to be more unsightly than lethal.

Thanks, mainegrower, it's nice to hear that it is likely damage not disease.

What is the best action to take with these stems? Prune the stems down to the next set of healthy leaves / side-branch? Do it now or wait until after bloom in a month or so (when I would normally prune it)?

I'd wait until your normal pruning time. Most of the leaves in the photo of yours do not look too bad. You can cut back to the point where you see a green swelling of new growth or just let the browned leaves fall off naturally. The latter course results in naked stems which won't look great, but if you pinch out the growing point on lower branches to encourage bushiness, it will soon fill in.

The extremely curled leaves on the neighbor's plant may mean that the stems themselves are too damaged to recover. Cut these back to a growth point on live tissue - might as well be done now.

Thank you very much for the advice!

Sorry to be a wet blanket. But your neighbor's bush is likely to have root rot.

Beyond that, the neighbor's droop is different than yours.

You neighbors is probably not root rot. Root rot usually kills the entire plant. Drought damage kills individual branches as does borer damage. Those curled brown leaves are on dead branches. They will not come back.

Your damage looks more like winter damage on areas more exposed to sun and wind.

Here is a link that might be useful: How to grow rhododendrons and azaleas.