The tl;dr version is that he's a younger Arsene Wenger with much more emphasis on drill than creative freedom.
Having looked into his time at PSG, it felt like he did a good job trying to manage the club; it was simply that for his methods to work, he required people to listen to him. It's a lot harder to do so when some of the key players in the squad the backing of the board.
His preferred formation is 4-2-3-1 or 4-3-2-1 (attacking triangle), but has been proven to be adaptable when required (4-3-3 with a defensive triangle at PSG being the most obvious case). His Valencia team, from what I could find, was focused on very fast transitions and slick teamplay (think Lucien Favre's Borussia Moenchengladbach and OGC Nice sides). His Sevilla team was built for counter-attaks, while his PSG side is only meant to attack and nothing else (but I don't really blame him for that).
If you believe the story that made its way around fan forums, he said that he will build the Arsenal team around Aaron Ramsey and Pierre-Emerick Aubameyang. This would imply that:
- Aaron Ramsey will play in central midfield with a role similar to how he plays for Wales: running from deep to capitalise on loose balls.
- Mesut Ozil and Henrikh Mkhitaryan will be playing out wide.
- Pierre-Emerick Aubameyang is our main forward. Depending on the formation used, Alexandre Lacazette will either start or play second-fiddle to him.
- Granit Xhaka will do much better this season; people know him for his long passes from deep. For whatever reason, Arsene Wenger did not use this trait of Xhaka's. I theoreticised that this meant that Xhaka was often put under unnecessary pressure because he wasn't being asked to play it long, instead choosing to look to play short passes. However, the way teams play nowadays, this meant that if he was not given enough time, he would very quickly run out of time and space to act, losing the ball and thus exposing us to transitions. This has at times meant that Mesut Ozil needed to come deep to play the ball, which ironically meant that at that stage of the game, there was no one sitting between the lines trying to play the ball in attack (at that stage, Alex Iwobi and Danny Welbeck stay out wide before cutting inside in the final third).
Beyond that, Unai Emery loves drilling, will focus on 'back-to-basics defending (Shkodran Mustafi and Granit Xhaka should prosper here) doesn't really like using his full-backs as overloading options, instead choosing to play them as inverted full-backs when they have the ball.
I am expecting a return to his Valencia days: a disciplined, well-drilled Arsenal that is able to press cohesively and work hard for the ball every second, and yet be capable of lightning-fast transitions.