Bumi vs Toph is probably one of the closer IMO. While he's got power, she's got tremorsense, which he doesn't, and metal bending, ditto.
In general the White Lotus almost all have a power advantage over their foes, but the Gaang often has more variety or newer tricks that the Order doesn't.
Zuko's one special move, lightning redirection, is likely wasted on Jeong Jeong who won't zap him anyway. So definite win to JJ, Zuko's got nothing on him even with his sun warrior training.
Katara vs Pakku, Pakku's probably still stronger, but if it's a full moon Katara'll win, if not she'll lose.
I think with all four elements under his belt, Aang should probably beat Iroh, this is one case where the Gaang side has the power edge.
If you added Suki, then she and Sokka might be able to handle Piendao, but not just Sokka, like NemeBro says that's a gross mismatch.
As a group, the two things going for the Gaang are possibly teamwork (the order doesn't exactly meet often), and Katara's blood bending. If it's not a full moon, then the Order wins.
Comet power amps don't matter too much, since they apply to both fighters in each case, but probably help the Order more. Jeong Jeong uses his to hover after all.