[Verizon HTC One (M9)] RuLEoF2:
Wow. You have a lot to cover. Not sure I can address all of your questions but I'm happy to offer my opinions. I'm a root user so my perspective may not be very useful to you if you intend to stay stock. If rooting is your plan, either device is a great choice and I strongly recommend TeamVenom's ViperOne ROMs.

Currently, I have both the M8 and M9. They are very similar with the main exceptions being the M9's vastly superior processor, camera and updated OS. I'm very partial to HTC. In fact, Every smartphone I've owned from day-one has been HTC. That's mainly due to how I was introduced to smartphones in the first place. When I started asking around, a coworker spoke very highly of HTC and specifically mentioned how they were more independent than other brands which allowed for more customization. He also said for that same reason, they were easier to root and got a lot more attention from developers as a result. So, in addition to being introduced to HTC, I was introduced to rooting at the same time. I've rooted every one since and can't imagine having a stock phone. I got the M8 in November of 2014 and it's been the best one yet by far. I couldn't have been happier with it.

To get to your primary question, one consistent trait that I've seen with all of my HTC devices is that they do have a tendency to get hot during downloads and when using GPS. Scary hot while while doing either and charging simultaneously. The M9 is particularly bad with this, which is no doubt due to that octo-core processor. The upside is the metal housing which acts as a heatsink, allowing for rapid cooling. The fact that the heat is so noticeable is evidence of this and a very good thing.

Other than the heat issue, I've been pretty happy with the battery life on the M8. However, I don't use my phone for music or streaming videos very much, but I do up/download files a fair amount. The battery will take a pretty good hit if I'm doing a lot of that. Because I don't really use my phone for music, I can't say much on that but what little I have listen to has sounded as good as my iPod (the only Apple product I own). What I can say in regards to sound is the external speakers are nothing short of phenomenal. Full-on stereo with an almost surround-sound quality. Definitely the best exterior sound quality available.

Though I've had the M9 for about six weeks, I haven't started using it full time yet. My M8 is still in great condition and perfectly functional. I had to replace the battery a couple months ago which is what prompted me to start looking for a new device. At first, I wasn't sure the M8 would survive the battery replacement, but it did and it's been better than ever. So, in the meantime, tweaking and modding the M9 to get it closer to my M8 has been a kind of side project.

As for brand vs brand, my wife has the Samsung Galaxy S5, so I can make a fair comparison to that. I've also had opportunities to explore iPhone, Motorola and LG devices. In general, even without root, I think HTC just does a better job with UI. Everything is laid out in a practical and sensible manner. The S5 seems like it was designed for a child. In addition to its cartoon-style UI, it's like they went out of their way to hide settings and features. Then, what little options it has are so limited that you really can't do anything with it.

So, that's pretty much all I have to offer. If you have more specific questions, I'll be happy to tell you what I can so don't hesitate to ask.