I think the key is balance, but it can work differently for different couples.
When I write a Bruce/Dick that is hurt/comfort (Wings Of Angels Trilogy Book I: Epidemic), generally I do write Dick as the wounded one because it brings out so much strong emotion in Bruce, but the reverse shows us a vulnerable Bruce. Out of the three pairings I’ll mention here, these two are the closest in power and equality, having balanced their work as Batman and Robin for years.
With Clark/Bruce ("Until The Yellow Sun Blesses You Again..."), there’s the power disparity, and so it’s very interesting to make Clark be the wounded (or more severely wounded) character, but if Bruce is the one to suffer the most physically, it’s interesting because of his strength of character and self-reliance.
With Diana/Steve (Stained Glass I: Shattered), you get the disparity of power and the gender issue thrown in for good measure. Also different cultures (Amazon/American). I’ve written mainly upbeat romance for these two, but am currently putting them through the wringer. ;) The balance is working there as in the first two chapters, Steve must do the protecting, and then it’s Diana’s turn.
Hurt/comfort as a genre can be a tricky balance. If you write too much hurt and not much comfort, you can exhaust and depress the reader. If you write little hurt and a lot of comfort, you get a different kind of fic in some cases. If you find the right balance, you can have the best of both worlds. :)
We all know that hurt/comfort is usually of the physical variety, but that often entails emotional h/c as well. Also, you can write purely emotional h/c, but we all have our kinks. ;)
I noticed that my hurt/comfort stories do tend to go long! :) My most recent h/c, Stained Glass I: Shattered is ten chapters long and does delve into Warrior Diana starkly in one chapter and then in more muted form in later chapters. You can do wonderful character studies with this genre.
Hurt/comfort puts characters through the wringer, but we the readers indulge in our guilty pleasure! ;)