On defense maps they are both good, but on offense Swann pulls ahead.
The main reason why Swann is better is because of his Hercules-tank micro build, which can start clearing bases much more effectively than Karax before Karax even rolls out his first Immortal.
Swann also has his very powerful bots calldown at 4 minutes, which can clear an attack wave plus any contested expansions or the first base on a map with less effort than Karax using his entire starting energy stock with a probe spotter or offensive cannons. They last for a long time, so you can use them at multiple locations.
For example on Chain of Ascension, you can kill the first attack wave, clear your contested expansion and then clear most of the first enemy encampment with a single calldown, which is more than what Karax can do with his starting energy.
Also, HH is least played commander because they are one dimensional and can get boring after a few games, but they don’t suffer at all because of lack of static defense. Mag mines, strike fighters, or top bar big calldowns take care of any attack waves. They also have a weak early game and many things counter reapers.