Zuko vs Azula
Like I said, Zuko was able to hold his own against a sane Azula before his dragon training (season 2 opening). The only reason why I'd give Azula the edge is because of her ability to play mind games with her brother. Zuko's swords make things interesting, as he can effectively combine firebending with their use. But Azula carries projectiles herself (see "day of the black sun"/"the eclipse"). Azula's cunning strategy gives her the edge. However, Zuzu isn't alone here.
Tonraq vs Unalaq
Unalaq is the better bender, Tonraq relies on his brute strength and athleticism more (like Father like Daughter). His feats ARE impressive, just not effective. Important to note that we never see Unalaq and Tonlaq fight each other unscathed and at 100%. Tonraq was taking out soldiers and took a hit from his niece and nephew before fighting Unalaq.
Tenzin vs Zaheer
Tenzin destroys Zaheer if fighting one on one. "Destroys" being relative considering airbending is primarily a dodge and evade type element. However, give Tenzin credit where it's due. Not only was he able to take on three benders on his own (until pli sniped him) but he did the best at drawing back the dark spirits in the LOK season 2 finale. Zaheer may be more cunning, but he has yet to demonstrate his skill outside of airbending (show don't tell).
Sokka vs Mai
If fighting one on one, Mai wins. Sokka is better behind the scenes. Mai can get a few hits in if she acts like a sniper, but she typically fights out in the open. Sokka is aware of his shortcomings and thinks outside the box to turn a match in his favor. (Beating combustion man, air ship slice, etc.)
Azula team strategy (more likely to fight their counter-parts due to justified overconfidence):
Azula would likely focus on Zuko and Mai would primarily protect Azula.
Zaheer is the "bait", jumping around to keep everyone unfocused and busy (mostly Tenzin).
Unalaq would focus on Tonraq.
Strategy for team Zuko (arguably more likely to think outside the box):
Tonraq focuses on Azula and Zuko focuses on Unalaq (at Sokka's suggestion), switching off every so often.
Tenzin provides support and contains Zaheer
Sokka stays behind the scenes and finds an opening to use his boomerang.