Cable PQ quality varies from provider to provider, city to city. The same company can have a great looking picture in one city and terrible in another. Your best bet is to use the Local Reception thread
for the city and the cable company you're comparing. They can tell you.
Yes, DirecTV has a little more bandwidth and tends to have better PQ than Dish for most cable-network channels. Broadcast network channels are rebroadcasts of local affiliates and that PQ will depend on the local affiliate.
Yes, weather is a factor. A really good thunderstorm or snowstorm can interrupt the signal for brief periods of time. A really well-positioned dish will mitigate that (tip your installer). For DirecTV, weather interruptions are less impactful on their legacy, standard-definition channels as they're on a different band. (I'm currently in Florida. Storms knock out HD channels, but not the SD ones). All that said, weather's really not much of a concern if you have high-speed internet. Most channels offer some form of live streaming to Cable/DSS subscribers. See a storm coming? Watch the stream instead of the satellite.
FWIW, I've had both DirecTV and Bright House - now Spectrum - simultaneously for a long time. Weather outages for DirecTV are brief. Cable outages can last for hours or days. I'd say the downtime between the two for any given year for me is a wash. HOWEVER.. power outages are a different thing. I have a generator. As long as I an power my DirecTV box and TV, I'm good. If cable goes down with a power outage, that's that.
For your fourth question, it all depends on your own personal preferences or tolerances. Users seem to like Dish's equipment better, but prefer DirecTV's PQ and 4k capabilities. Customer service is always a dice roll. I see horror stories, but have not had anything but kind and efficient customer service. That said, I rarely call them for anything other than adding or removing HBO, Showtime, etc. Like cable, service calls are going to vary by city. The DirecTV contractor in Detroit was outstanding. Here in Tampa, I've heard otherwise now that AT&T crews are handling things. Again, YMMV.
Yes, NFL Sunday Ticket is quite an ace for DirecTV. There's no other way to view out-of-market Sunday games in their entirety. A lot of defectors from D* to cable have found NFL's RedZone channel sorely lacking. Especially if you're a fan of a particular team on a Sunday where RZ does precious few live look-ins. It all depends on what your football is worth to you. There are rumors the NFL will opt out of the remaining years on its NFLST contract with DirecTV to front its own ST streaming service. Count me among those who doubt that, but still think it'll happen at the end of the contract.