Which should I get first? Which is better and why?
I already have OWB but I don't think I would enjoy DM.

i'd get honest hearts. i didn't exactly like it better than lonesome road, i just find it funner. there's also lots of good loot. Lonesome road also has good loot, but honest hearts has more practical guns that you'll be more likely to use. i look forward to honest hearts the most out of all the DLCs, and i just totally love the environment, theres nothing else like it in fallout. it really depends what you're looking for. lonesome road is heavier on the action for sure, and theres a lot of impressive stuff happening in it. not to mention it ties up the courier's story and has some lasting effects in the mojave. but Honest Hearts is great for survivalists and its just all around fun to play and replay, in my opinion