The answer to this is more complicated and nuanced than people would like it to be.
In reality, its because both Arsenal and Man City play very differently to us. The role of their inverting full backs and the way their centre backs step out of defence creates a crowded central midfield area. It leaves them vulnerable to attacks down the flanks. However, they keep the ball so well, and use the tactical foul so effectively, that they're rarely caught out.
Ten Hag seemed to be trying to move in this direction early on this season but the team either couldn't or wouldn't adapt. In that first game against Wolves we tried to squeeze up the pitch and had Shaw inverting. However, Wolves beat our high press constantly and Nunes exposed our lack of mobility in midfield and ability to keep the ball.
The way that Pep and Lego Pep play is dependent on keeping the ball and shutting down counters quickly and effectively. If you can do that you can force more attacking players onto the pitch. Which is what both do. On paper City play 3 at the back but that's partly because one of their centre backs effectively plays as a defensive midfielder and their forward line is so wide, and occupies so much space that it creates problems for opponents.
We just can't seem to get it right. Ten Hag IS pushing the midfielders forward into similar areas that the City and Arsenal players occupy. But even though we are forcing a high number of turnovers, statistically, we aren't capitalising enough to scare opponents. Invariably we have good 20 minute spells, run out of gas and then lose control. End up retreating deep and hoofing it because the system breaks down. Plus, due to the bad form of our wingers, Ten Hag has committed to using the full backs to create width and they're inverting much less. This means its much harder to hold the ball in midfield and gaps open up routinely in our midfield shape.
We're kind of a halfway house between pre-Van Dijk Liverpool and pre-last season Arsenal. We are playing in a way that generates a high number of chances but is defensively unsound. The coach needs to decide which path he's going to take. If we're going to go more in the Liverpool direction, we need more pace and power in midfield and more commitment to using the fullbacks as attacking outlets. If we're going to go back to a more Ajax like way, then we need to get the timing of our press right and our wide forwards need to become vastly more productive and able to win 1v1 duels without overlapping full backs.