Within the broad classification of azalea (evergreen sub-division in this case), there are 100's, maybe 1000's of different varieties. These vary in their ability to withstand winter cold and wind.There's nothing in the photograph to suggest anything more than a difference in hardiness. With absolutely no information about your location, varietal name of the azaleas, winter lows, etc., etc. no more specific information is possible. In any case, unless there's a reason for applying fertilizer, don't. Cutting back into live wood may produce bushier plants, but no guarantees.

Both azeieas are Johanna variety, purchased and planted 3 years ago in southern ct.

Same location, same variety, one struggling the other not. Purely guesses, but:

0ne may have been mislabeled or did not establish as well as the other and thus was less able to withstand the past winter. This is usually listed as a Z6b plant, so would be marginal for much of southern CT. One on the left exposed to more sun and wind. Even if very slight, such differences can matter more than you'd think.

both look as if they could use some pruning to remove dead stems and to .encourage bushier growth. You might also consider a simple soil test to determine if fertilizer is needed and the pH is within acceptable range.