I can't claim to know what our training methods are but I think I have a basic understanding of what Mourinho focuses on in comparison to someone like LvG.
A couple of years ago, under van Gaal, we showed that we were, somewhat, comfortable being pressed - obviously, Fellaini played a big role in beating the likes of Liverpool, Spurs and City. We've missed the big fella a lot in the games against Pool and City. With Mourinho, there seems to be less focus on being comfortable on the ball and more importance assigned to how good a player is off the ball i.e. how we respond defensively when the opposition has the ball and how the attackers move when on the counter. Many have questioned what our style/philosophy is, my take on this is that we're a team that prefers the opposition to have the ball. We'd like to win the ball in our half and the ideal scenario/s is/are for:
a) someone like Pogba to carry it forward
b) long ball towards Fellaini
c) get the ball quickly to Martial/Rashford and have them carry it forward
Our biggest issue last season was goal scoring, credit goes to our management/players for sorting this issue out.
I can't see us preparing/drilling to play against the likes of City, Lverpool, Spurs etc. every week as you don't play these teams very often. Vast majority of the premier league is going to:
a) sit back at OT
b) attack in a calculated manner when playing away from OT
So, I imagine we spend a lot of time preparing to play against the likes of WBA, Palace, Bournemouth etc. We seem to have two plans, one for a team parking the bus and other for teams for likely to have more possession than us. We're not like the other top 6 teams who have one style against any team they play. Mourinho is very good at adapting to different situations and even yesterday, we were inches away from equalising with 10 minutes remaining - in what was an evenly contested game.
Mourinho has shown over the years that he knows how to play against the best teams but his style relies upon individual brilliance and defensive solidarity. Against Watford, we had three guys produce moments of brilliance and we defended very well till the penalty. Against Arsenal, we were defensively poor but still had moments of excellence from our front four. Yesterday, we were defensively solid but, other than Martial on two occasions, every other attacker failed. As bad as it sounds, I don't think we'd spend too much time trying to improve our ability against a pressing team as you don't play this type of opposition every week. Rather, Mourinho would like for those comfortable on the ball to take responsibility from those who lack the ability and composure on the ball. It's just that we don't have many of those players in our squad. If you look at his signings - Bailly, Mkhi, Ibra, Pogba, Lindelof and Matic are all very comfortable with the ball at feet, so it goes to show he identified that we had a lot of players who lack this ability and has attempted to resolve the issue.