Aww, I gotta’ choose between BG and Harls in a fight? Mmm. I like them better as BFFs. 
M’kay, welp, if I gotta’ choose, I choose my gurrl.
Now, while Harls is a super formidable fighter, she’s not necessarily skilled in any particular fighting discipline, instead relying on tricks, gags, and unpredictability as an edge. However, these tricks are usually employed to get her out of a fight, and not necessarily used as strategy to win the fight. Sure- she’s got the gymnastics ability, but ultimately that skill translates more towards aesthetics and doesn’t really payoff as actualized, sustainable hand-to-hand combat prowess.
BG, however, is another story.
Back in her debut days (Detective Comics #359 and forward) Barb had achieved the level of brown belt in karate along with dabbling in some of the other martial arts styles. But that was before she started running across the rooftops of Gotham tracking down baddies with this hand-to-hand combat legend and his super bada55 ward.
Under the Dark Knight’s tutelage, Barb gained invaluable fighting skills after learning the foundations of Judo, Jui Jitsu, Kung Fu, weapons fighting (those Batarangs tho), Boxing, and Escrima.
During the Oracle years BG’s wheelchair never inhibited her spirit and will to fight, She was able to tune up her Escrima work via her skills-building sessions with one of the DCU’s most amazing fighters, Dinah Lance.
Moving forward into the New52 and Rebirth years, Barb was able to experience new aspects of hand-to-hand via time spent with martial arts master Fruit Bat.
During this time my gurrrl learned all new ways of applying her fighting skill-set during confrontations with her opponents. She also got to cut her teeth in some MMA style cage match fighting, along with many more intensive study sessions with Dinah. She came out of this era of her life a completely focused and super fearsome fighter.
Harls, I truly love you with every bit of my heart, but my fellow amaze GirlBat @TheWifeOfJasonTodd called it correctly- I gotta’ go with BG in this match up, and all of the other ones to come. Yep.
+ 
= BFFs
