Neither. I'd say overall diphenhydramine (Benadryl) makes me feel worse, however, I try to avoid H1 antagonists.
Doxylamine is said to have a 9 hour half-life, however, diphenhydramine can range from 4 to 8 hours depending on the individual.
Chemistry wise, they are both similar as well.
Interesting side note, doxepin (Sinequan) is 800 times more potent than diphenhydramine, and at 75 mg almost completely inhibits histamine release from some tissue stores.