巧み。たくみな： schmoov: a clever ad slogan, slick flattery, adroit political manipulation,
巧み：たくみに： physical OR mental finesse : a PR man finesses a hard question with a bullshit answer so slick that the reporters don't realize they got hoodwinked. A boxer with fancy footwork. Also, to do something deftly (a movie deftly interweaves 3 stories: a teenager deftly juggles church life and gang membership, etc.)
器用な：きような - this is more positive than たくみ。 it means someone like a kung-fu fighter that can jump around and not get kicked, or a pianist who plays hella difficult pieces without any fucked notes. There is also an implication that the person can improvise!
俊敏な：しゅんびんな： ａｇｉｌｅ， ｑｕｉｃｋ－ｗｉｔｔｅｄ．ｐｈｙｓｉｃａｌ ｏｒ ｍｅｎｔａｌ???
THESE GUYS, I DON'T KNOW WHAT THE DIFFERENCE IS. CAN YOU HELP ME?