Two separate analyses, but here's my take.
Gase
He's a young but very capable coach who had to learn about being a head coach. Unfortunately, he surrounded himself with nothing but other young coaches and lacked a bit of perspective. The few veteran coaches he had were not fonts of wisdom. Belichick started similarly, but once he matured and stopped the two-steps-forward-and-one-step-back dance, his talent took over and he was successful. Gase has a chance to develop like that, although anyone becoming the next Belichick is unlikely. For him the key will be how he learns from his mistakes and how he is able to succeed as a man-manager rather than an X's and O's guy. Despite massive injury problems, Gase flashed some ability.
Tannehill
One could say that he's already proven he's a good QB, and up until a fateful fluke low hit by Arizona, he was shaping up to be an ironman of a QB. But reality is that he has missed a LOT of games, is now older, and has had mild success under a bunch of OC's but never really put together any elite seasons. For him he needs to stay healthy. Having been sacrificed behind horrible OL's in Miami, he stands a chance to shine in Tennessee, where their OL is among the best in both pass protection and run blocking. If he stays healthy and isn't successful behind that OL, then its probably time to face the fact that he's an average NFL QB, not bad, but not special either.
Fans love to vilify people, and the QB and HC are usually the two biggest targets. They get touted as HoF type talents when the team has moderate success, and get blamed for everything bad about the team (and weather, and everything else) when we start to lose. But in reality, these are guys who have high impact on the people around them, but they're not the entire team. Both of these guys have flashed success. Injuries, bad OL's, poor assistant coaching hires, etc. have contributed to how they are perceived. Each of them still has a reasonable chance to succeed.
If they succeed away from Miami it only proves what many of us have been saying all along. Tannehill needed a decent OL. Now he has one, if he succeeds, that's my guess as to the reason why. Gase was a young coach who needed to mature. If he has a healthy team and succeeds away from Miami, those would be my guesses as to why. Given that we never had healthy players nor a decent OL, it would point to failure in the player selection and training.
We're moving in a new direction, and I support that. If it ain't broke don't fix it. But the Miami Dolphins machine was broke. So let's try to fix it. No disrespect to Gase and Tannehill, but it didn't work. Einstein's definition of insanity is to keep trying the same thing and expecting a different result. I think we're doing the right thing by trying a new approach. Hopefully it brings us an elite QB in 2020.