Just a hypothetical because I see fans still think the team's problems are due to the players, not the coaching. While the there were drops last night, I don't think it would have made a difference if they caught those passes. The team look confused, unfocused, undisciplined and just plain lost. It looked like the usual school yard football from a Tomlin coached team. On to the hypothetical situation. How would the Steelers and Patriots do if they switched coaches as of now(the HC's OC, DC etc... would follow their coach)? Give them this year to fine tune how they want the team. Start in 2020 as to how you think the team will do.
IMO, Belichick will do a small amount of house cleaning. I believe he will get rid of Dupree(but then again it's Belichick so he could probably get something out of him). The rest of the original team will mostly be in place. Belichick will have the team focused and hone the fundamentals of the game. A lot depends on how BR will take it. Belichick demands his QBs to know it all. I don't know how that will fly with BR. It will be Chickillo and Watt as the starting OLBs. An upgrade at TE will probably take place. The WRs will change. Expect Belichick to acquire disciplined, quick, slot receivers with good hands and strong fundamentals. Schuster will stay, but I am not so sure about the others. I would say Switzer, but he doesn't exactly have the best hands or catch radius. I think he would keep Washington so he has a vertical WR. There could be some changes in the safeties. Overall, I believe Belichick will work with what is there. The Steelers have athletes/talent, but they have no idea what to do on the field or how to utilize their athletic/talent skills. Their fundamentals appear to be lacking at times. Belichick will remedy that. One thing is certain, the players will know where to be and the plays called. Overall, the Steelers would be a powerhouse under Belichick.
Now for Tomlin. The team will show signs of fading immediately. No game plan and a happy-go-lucky practice will soon show its results. Tomlin will insist on finding splash players over coaching, game planning, fundamentals... The Patriots aren't a team with a lot of talent like the Steelers. Tomlin will talk his talk, but it won't do any good. The good thing is Brady is the QB. Brady will do as much as he can to keep the team afloat, but that will become more difficult as time goes on. I could see Brady retiring or asking to be traded to the Steelers following the 2020 season. Overall, the Patriots could make the 2020 playoffs due to Brady, but they won't go far. 2021 will result in missing the playoffs.