By the time of The Legend of Korra, the title Avatar: The Last Airbender had become somewhat innacurate. Aang was not the "last airbender" afterall, going on to father a son Tenzin, who himself continued on the airbending legacy before the Air Nomads were born anew. The presence of more Airbenders only made Aang's natural talents for the elemental martial art clearer, and it's quite possible that he was the greatest Airbender viewers ever had the fortune to see on screen. To truly earn that title he would need to be better than his greatest competition, Tenzin, and figuring out which monk is the greater master will be no easy task.
What is important to keep in mind at the forefront of any comparison between the two Benders is their difference in age for the majority of the audience's exposure to them. Whereas Aang was biologically a 12 year old boy throughout The Last Airbender, Tenzin in The Legend of Korra was a middle-aged man with a family and a lifetime of experience under his belt. Regardless, Aang was the youngest ever recipient of Airbender mastery tattoos and proved he could go toe-to-toe with adults countless times throughout the series.
What Aang perhaps best displayed was an aptitude for creativity, always striving to conform to his pacifistic beliefs with clever thinking. He most often used his powers to amplify his physical movements, reducing the air resistance around him for lighter and faster evasive tactics and tall leaps that kept him just out of his opponent's reach. Such creativity allowed him to create a rapid-moving air scooter or to super cool lava so that it solidified into stone.
At the same time, Aang was not lacking in raw power. He frequently pushed back huge swathes of enemies when forced into a confrontation, and as the series progressed, his ability to toss around large amounts of weight with his blasts of air only increased. He could sent a cabbage merchant's cart flying down an alley, an entire trebuchet careening over a cliff or even knock massive iron doors off their hinges while invading the Fire Nation palace on the Day of Black Sun.
But Tenzin is no slouch in any of these departments himself. When it comes to raw power, he may even have the superior feats to Aang's, as the first season of Korra showcased that he could whirl himself around on a wind tunnel with such power it cracked concrete with the bodies of those he flung. With enough leverage, he could even blast a mecha tank straight up into the air and onto a rooftop. The stodgy old master even managed to improve on his father's air scooter invention by crafting an air wheel technique that was even more practical. The air wheel could defend Tenzin from projectiles while he rode it, and it seems he took everything Aang did and improved on it.
However, there were still feats Aang accomplished that Tenzin just couldn't. Cooling an entire wall of lava with a gust of wind was a feat Aang accomplished Tenzin never even came close to. Looking at Aang's life after he TV series reveals even greater feats Tenzin could not replicate. Aang created wind tunnels beneath him that essentially allowed him to fly without a glider. In his pursuit of Yakone, he even showcased a much larger air scooter that, while not as defensive as Tenzin's air wheel, tore open the rooftops he road across with such speed he outpaced Yakone's head start.
The important thing to keep in mind is that this is not simply a comparison between a father and son, but a comparison between an Avatar and non-Avatar. For all of his talents and lifetime of diligent practice, there are few Benders ever capable of reaching the level of a fully realized Avatar. Aang takes the top spot when it comes to the series' best Airbender, but Tenzin comes admirably close.