Hey bro, this was my path exactly although I went from htc 10 to mate 9 pro rather than normal mate 9.
It all comes down to how often you listen to headphones, as the headphones output (loudness, bass delivery, power) is definitely not in the same ballpark as the 10. Having said that, it's decent sound but nothing to brag about. The speaker set up on the mate however is very similar in function and quality (maybe even a tad better). Lastly on sound, I find the Bluetooth sound output is also a bit lacking but that could just be a placebo affect from the difference in headphone sound.
Having said that, everything else is an upgrade: battery life, the screen on the pro is better, camera, speed of the device granted the 10 is no slouch either, software is ugly and needs a launcher/icon pack lol but software functionality is on point for the most part--emui5 finally adds to the Android experience rather than takes away. But yeah, despite the headphone sound it is an upgrade in every other way in my opinion. The only think I'm stuck on is trying to figure out how to get Spotify on the lockscreen while music is playing. It can be done via app but I'm trying to figure it out natively
Feel free to ask any questions though bro!