I'm a long time Adobe Premiere Pro and more recently Final Cut Pro X user. It really depends on what you want yo achieve but I found DaVinci way more powerful for certain projects/workflow. I stopped working with Adobe software because of the subscription model and some reliability issues along the way and on a cost basis Final Cut Pro X seemed a much better solution for my simplest projects. Again, I just cut and graded my first project in DaVinci (a music video shot with a RED Epic Dragon) and it totally rocked! (and I'm talking the free version). In the end they are just tools and we work with those that make us feel more comfortably to get our work done.
It comes down to what works best for every specific project and I think that there's nothing wrong to have a personal preference for certain brands/equipment for whatever reason there is. It is all about choosing and mastering tools for your craft and you have to choose a few. I made my choice, but that doesn't mean that it will work for everyone nor everything out there. I've used many cameras for my projects: from Canon XL1, Panasonic DVC100 and Rebel T2i to RED Epic Dragon (including Sony and Nikon cameras), and as you've said, all of them has (or had) their own set of strengths and weaknesses. In the end, I just share my point of view and what has worked the best for me so far, but again, I'm not pretending that it has to work that way for everyone. On the other hand, I'm curious to know why you prefer D750 over C100 as I'm always open to give things a view from a different perspective.
RAW varies from every camera or platform available. Would you please elaborate? What do you plan to do? What do you want to achieve? Have you ever shot RAW format before? Is there anything specific that you want to know about shooting RAW?
I've used a Nikon D750 very little for video and I'm almost a Canon guy, so I'd go for Rebel T6i. I think it is the better choice for video anyway and good enough to keep you in the path of learning. I've never personally used these specific cameras so I cannot give further advice. Have you ever considered other options? I bought a Sony a6000 almost a year ago and I'm under the impression that you can get a much better image from it than any Canon DSLR in that range. For me it is a great camera, I've used it as a B-Camera to a Canon C100 under controlled lighting environments. Just a thought.
The purpose to have different lenses is to make images with different requirements and looks. 75-300 won't replace your current lens kit, because those are very different focal lengths. Perhaps you'll want to buy STM lenses, they are inexpensive, have a good quality image and add autofocus features in video mode (I don't know exactly if your body has autofocus features with STM lenses). There is no lens that can cover "all needs" so, having a set will be useful to you in the future. I remember shooting a project 5 years or so with a 60D mixing 720p60 and 1080p24. I used InstantHD to upscale 720p material and that project was mastered at 1080p. I also made a 480p (SD) master and everything looked amazing, it was almost impossible to notice difference in quality. It wasn't aired in TV thou, it was made for web and showed in public in a commercial stand.
Quality is very subjective, it is all about what your clients value most. You can name it: sharpness, detail, color depth, dynamic range, lighting execution, concept, writing, art direction, direction, performance, edit, color correction, post production, etc. All of this contributes and you have to understand what are your clients expectations when they talk about improving quality. Changing the camera won't make you instantly a better filmmaker, dp, producer, etc. It can contribute to improve some aspects but first you'll have to understand that with something that can be seen as very simple like changing the camera, comes with some other challenges because every camera performs in its own unique way. Also keep in mind and educate your clients about how everything has a cost and, based on what you have said before, perhaps their budget has no room to move up for better production values. If you decide ultimately that changing your camera (buying or renting) is the way to go, keep in mind what kind of work you'll be doing and go for a camera than can keep you covered (you mentioned slow motion, very curious to know why you are thinking in a scenario where you'll be matching two very different cameras like 1300d and 5D).