Honestly, it's hard to choose because both shows have more differences than similarities.
Similarities
-Both have tragic, flawed, emotionally screwed protagonists
-Both shows have a violent, surreal dark tone
-Both have brutal, menacing overarching main villains
That's where it ends for me at least. The thing is
Daredevil felt like a more serialized, grander series with a dark, gritty superhero style that had just as much substance with awesome performances, great storytelling, jaw-dropping twists, etc.
Jessica Jones, while based off the Alias comics, was a more subtle series that was a psychological drama with a film noir structure, equality stellar performances, good twists and some action thrown in here and there.
I loved both Kingpin and Killgrave. Easily the best MCU villains after Loki and Winter Solider. Both brilliantly acted and wonderfully realized antagonists with well written backstories and motivations that are understandable as they leave a massive body count throughout both shows. Back to the main heroes, Matt and Jessica are great characters, both played by very gifted actors who simply ARE the characters, performances that feel organic and
real. I mean, that first scene in the confessional during DD's first episode still gives me chills and Jessica breaking down after shooting Luke with the shot gun as she confesses her feelings for him...awesome stuff!
I like the "Law & Order" aspects of DD but the main focus was definitely more on the superhero theme, which of course, I enjoyed. The action scenes in DD were marvelous (puns away!), some of the best I've seen in ANY action/superhero show, movie etc. That one take final fight in episode 2 is STILL legendary in terms of execution, direction and choreography. Like many have said, that's what made DD essentially the more entertaining show since it was more action orientated. But it makes more sense since Matt/DD is a trained martial artists with allies and villains ingrained in that style of combat while Jessica, Luke, etc. are street brawlers with super strength, so I actually like the difference in action styles which give the characters more of their own personalities. Not that Jessica Jones didn't have good or memorable fights, I still think the bar fight her and Luke was hilariously entertaining from a story progression stand point as they discover each other's powers. Not to mention, the fight between her and Luke as well as her and Simpson in her apartment were pretty brutal. Not as brutal as DD looking like he might get sliced in half as a ninja drags his bleeding body toward him but you know what I mean.
I have to say both also have a great supporting cast/characters. Yes, even crazy twin sister who doesn't know what the bad place she's talking about. Sure, a rather dumb, illogical character but she served her purpose by reminding Jessica even the most naïve and annoying are worth saving.
All and All, DD and JJ are both great shows, full of depth, maturity and emotional resonance. I'd say DD is only slightly better do to stronger writing, amazing visuals/direction, superb action set pieces and felt like a 13 episode movie culminating with the Man with No Fear in his red costumed glory. JJ was more character driven while only referencing and down playing the superhero side of her character. Ultimately, she was a different kind of hero than DD who had to overcome some overwhelming emotional turmoil more than Matt. She didn't have the luxury of being this masked vigilante that won the hearts of NY in the papers by season's end but was the ultimate underdog who was out to stop a man who robbed her of her self-worth. It was more a story of personal triumph than a cautionary tale of bad place's Kitchen's crime syndicate.
Daredevil:
A-
Jessica Jones:
B+
So I guess I pick DD, huh?