The Cap gets a bad rap, but that's due to the writing of the show he was in. It's like Aquaman; quite badass with useful powers, but in the wrong hands the character just feels contrived and stupid.
Gimme a deconstruction of Captain Planet and his powers, and he'd probably be able to take on any Avatar. Depends who has greater control of the elements.
Well let me see...
Captain Planet has domain over the five elements of: Earth, Water, Wind, Fire, and Heart that have been combined together and multiplied.
Along with this Captain Planet has super strength capable of lifting hundreds of tons, infallible aim, super endurance, and super durability (he once broke a drilling machine with his body). He can also fly at subsonic speeds (or super sonic if he transforms into electricity) though an arguement can easily be made that he can move at super sonic speeds and ultrasonic speeds when he turns into electricity.
Captain Planet is empowered by the elements including can be empowered by the sun.
Along with this Captain Planet can control every element, creating and moving it about along with being able to commune with animals. He can transform into fire, lava, electricity, trees, and wind to create tornados. He cannot use his element control on manmade substances or substances that have been poluted.
His weakness is to manmade polution but the major materials that harm him is oil and industrial waste, and the polution that harms him the least is raw garbage, for the most part the more toxic the substance is for humans and animals the more toxic it is for him (for example the industrial waste I refered to would instantly mutate or kill a person). He has been shown surviving in mildly poluted environments (smog) and radioactivity. He is completely unaffected by heat as he is more then capable of surviving in the earth's mantle.
You are also right Captain planet as the show went on was terribly weak to standing perfectly still and letting the enemies get polution on him... but in early episodes he was often shown capable of defeating a monster completely made of SUPER polution (admittingly he couldn't touch it normally but neither could we) and surviving in a smog filled environment without serious weakness... where the villains had to try hard to surprise Captain planet. The WORST stupid excuse for Captain Planet to lose was when he turned into a tree to stop a super threshing machine, even as a child I thought that was weird.
Either way I know Captain planet would beat Korra... Where is this mound of toxic waste Korra can burn?