Doesn't every manager play 'Championship Manager' to an extent? The way Weir set us up wasn't disimilar to the formation that Clough plays. He's playing many of the same players and the formation has been Weir's 4-5-1 too.
Three big things for me which have been the difference:
1) Possession v High Tempo: Under Weir we tried to control possession and dominate teams this way. Clough has allowed teams to play in front of us. Clough came into a team with confidence at rock bottom and through the FA cup got the team to become confident in allowing the opposition to keep possession, but only where we allowed it. Clough set us up to counter teams with pace. Weir set us up to maintain possession and keep the ball, ultimately this meant that teams could press us back and force a lot of errors. Errors which have seen us also get caught out under Clough, but he's worked to minimise these individual and collective errors.
2) Discipline: The key though has been that the game plan under Clough has been firm and fixed. He picks a starting 11 which is his strongest team. Almost all managers before him in the last 10 years have done the same, but have chopped and changed after 60 mins. Clough has had confidence in his starting 11 to do the job
Ultimately, this has comedown to discipline. Each and every player knows his job and his team mates job too. They're a collective, well drilled team.
3) In fairness to Weir, Clough had time to assess the team before the transfer window and also allow the players not performing to raise their games. Brandy and Taylor didn't. Flynn and Murphy did. Clough, once he'd assessed the players, saw fit to bring in quality like Scougall, Brayford and Harris. All of which contributed with pace. We don't know how Weir would've handled the Transfer Window, we only know that Clough worked it very well, with the exception of Billy Paynter, Clough's work in the transfer and loan markets was excellent. But then Weir was no dummy, bringing in Coady, McGinn and Baxter.
Weirs unforgivable signing was Marlon King, but as I found out from within the club, this was not just Weirs decision, but a club decision.
Weir made errors, I'm not sure he was necessarily pig headed as the formation has worked under Clough. I think his execution was poor. For example not realising at Bradford that they were vulnerable on the Counter attack and that Taylor didn't like the ball into his feet with his back to goal, he wanted the ball in front of him.
Weir should take some blame of course, but as always, so should many of the players who didn't perform. Flynn, Doyle, Coady, Taylor, Murphy they were all poor compared to the same players that ended the season (Taylor apart).
Clough, should be praised highly, he could be forgiven for doing as
Harry's Game suggested and forget the FA Cup, he could've taken no notice of Morgan, he could've arrogantly walked in (like others before him) and dismissed players. Clough has given chances to fringe players and quickly sifted through to find his team. Its why he is looking like the best manager we've had in my lifetime.
Weir lacked experience, didn't know when/ how to get the best out of his players and ultimately wasn't flexible once the players went over the white line. To a greater extent, neither is Clough. Clough is just much much better at the job than David Weir.