KILL MOVES
The new engine they brought in with Empire: Total War (Warscape, as it is called) is incredibly flawed. It was designed for musket battles and artillery, hence why the projectiles and missiles work very well. However the Warscape engine was not designed for melee combat, and 'kill moves' (set piece animations done by stuntmen) were introduced as the SOLE way of soldiers attacking, meaning that once a 'kill move' starts it cannot be interrupted, vastly limiting the amount of scenarios that are possible; in earlier total wars 'Rome I' and 'Medieval II'' the engine they used (I don't think it really has a name) allowed for lots more variables. For instance, soldiers could be knocked down and then get up and soldiers could also interrupt attacks. On top of this, units could both attack another (1 unit) at the same time. This is a major issue, in later Total War games it is theoretically possible for a single peasant to be surrounded by hundreds of enemies and yet (if he keeps getting lucky and kills them) tie them up (occupy their 'attention') for a battle deciding length of time, due to the fact that only one soldier can attack him at once meaning that all the soldiers stand there and do nothing whilst one soldier engages. In Rome I, if a unit was surrounded it would die much quicker as all units within striking distance could all attack at once. This may not sound like that big of a deal but in practice, it looks stupid and totally kills emersion. Also, kill moves (from a spectacle point of view) dramatically worsens the melee combat; There is a fixed number of 'kill moves' to view, after a few battles you'll have seen all of them and they become boring. Because of the kill moves soldiers also slide around (without the 'walk' animation) trying to get into position to start the kill moves, making it look like the floors are too slippery or something.
LACK OF UNIT COLLISION
In Warscape games there is no unit collision, only an illusion. In Rome II the units do not push and shove at each other like they did in the original, only statically poke each other with their swords in animations that lack any vigour. In Rome I when units charged they would all surge into the enemy unit visibly pushing into it, forcing it back, bending the main battle line. In Warscape games all they do is stop the units from colliding artificially: when a unit charges another the first rank starts fighting but the rest just all stop dead in perfect synchronisation, giving the impression you're commanding robots rather than actual people. In Rome I, each individual soldier reacted at a different speed to an order giving the battlefield a much more lifelike feel.
These are the two biggest flaws, in my opinion, there are many, many more.
Many of these points come from Reynold Sanity's video, Rome II One Year On:
https://www.youtube.com/watch?v=dy5GRaHzFnI
A lot of the deep flaws come from the engine and bad design decisions like removing guard mode and streamlining the campaign. In Rome I you had this almost RPG-like way of building up cities from tiny villages into massive metropolises (in my opinion) this was a better system, why can't a small town become large if you wish to invest time and effort into it, and different provinces (cities) still had value due to base farming and trade resources (that weren't as valued as they are in the recent TW's but still were useful). They also removed 'loose formation' from Rome II (as far as I know) from a lot of the units which is absurd if you ask me.
Don't take this a godsend, I may have made errors or mistakes (I don't play the newer Total Wars as much). Feel free to disagree, as long as you're polite about it.
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-V