Hmm, I had a baby who slept very badly (she used to wake at least once an hour, every hour, for several months), and it was very, very hard. I did end up co-sleeping because I was utterly exhausted, and in the end, that turned out to be the best solution. However, it was torture in those first few months.
However, I have also suffered from insomnia, and that is incredibly stressful too. It's hard to explain the frustration that being unable to sleep can cause. You can start to feel that you're on the verge of insanity after a while. And you can start to wonder if you'll ever be able to sleep again.
I'm not sure if either is worse, tbh, it's just different. And as others have said, it really isn't a competition.
If your DH is awake anyway, couldn't he deal with some of the nighttime wakings? Does your baby really need to bf in order to settle again, or is that just what works most quickly?
I feel for you both. Sleep deprivation is horrendous. :(