As the owner of a detailing business that focuses solely on vehicular interiors, hopefully my input will help; I too have both brands of machines: the Aztec Hot Rod and the Mytee HP60.
I started my business with the Aztec being the single most expensive piece of equipment I purchased. Before dropping almost $700, I performed extensive research and compared tons and tons of machines. I was super impressed with the length of the Aztec's power cord (50' instead of 25'), the length of the vac/solution hose (16' instead of 15' (yes, that 1 foot makes a difference)!), and the water lift when compared to the size of the machine. Overall, I used mine for almost a year and I couldn't have been happier with the machine's performance. I will say that the PSI isn't as high as it should be, but it does get the job done; you just have to pass over the carpet one or two more times than you should have to.
Now, onto the Mytee: I just ordered the Mytee HP60 last week and I have used it a few times now. This thing is a wicked beast! The PSI is double that of the Aztec and the vacuum motor is extremely powerful, but the power cord and vac/solution hose are both shorter. The Mytee has about 35" more water lift than the Aztec, but also draws more power which may be challenging if you're powering the machine with a generator (which I am). One of the largest and most significant differences between the two machines is the heater: the Aztec heats the entire 1.5 gallon tank of water at once, then blasts the water through the line, whereas the Mytee has twin inline heaters that keep the water in the tank cool and heat it as it travels through the solution hose.
I should say, though, that Aztec's customer service is superb, and Mytee's is not as professional as it should be. Overall, both machines have their advantages and disadvantages depending on your business's needs. If you can afford to spend a little bit more, invest in the Mytee, but if you're just getting started, the Aztec is definitely the way to go.