Both modes are FSK, and both have the same effective data rate (72 data bits in about 50 seconds), but there is one very big difference between them: bandwidth. JT9 is 20Hz wide. JT65A (the mode commonly used in HF) is 180Hz wide, JT65B (often used for 2m EME) is 360Hz wide, and JT65C (often used for 33cm and up) is 720Hz wide. Why does this matter and how does it relate to which one you would use on which band?
The first reason is noise. The power of the natural noise we receive is proportional to the width of our passband in Hz. If we can make a signal narrower, and the receiver filter narrower, while keeping the same signal power, the amount of noise goes down proportionally and the SNR goes up proportionally. This is basically free sensitivity!
The second reason is stability. Given the first argument, you might think that JT9 is always going to be the best choice for a low-data-rate, high-sensitivity mode. But to receive a message using an FSK mode where the tones are only separated by 1.75Hz, the transmitter and the receiver had both better be stable to better than 1Hz. Even on HF, not everyone is that good. As the frequency goes up, it becomes borderline impossible. JT65A has a tone spacing of 2.7Hz, JT65B 5.4Hz, and JT65C 10.8Hz. That makes them approximately 1.5x, 3x, and 6x as forgiving to drift as JT9.
So for MF and HF, where you want to be heard over the QRN and frequency stability isn't a big problem, JT9 works great. For higher frequencies, where the natural noise generally becomes less and less, and frequency stability becomes more and more of a challenge, JT65 is more suitable.