Not ready to play yet but I've re-read Tilly's Very Bad Day and see some obvious differences in the rules.
In Deo Veritas (IDV) has dice rolled for combat and saves always 'hit' on 4+. What gets modified is the number of dice thrown. Single dice are rolled for disorder, cohesion and army will tests and these have modifiers. Tilly's Very Dad Day (TVBD) use resolve dice. Each unit starts with a certain resolve. Ordinary pike and shot units have a resolve of 4, for instance. Whenever units roll for combat or anything else, they roll one die for each remaining resolve point. When resolve is down to zero, the unit routs. Lost resolve can be restored by routing enemy units or by generals rallying the troops. TVBD has a one page QRS, with examples of play on the other side. There are basic rules and many advanced rules. I will use one advanced rule to show troop ratings since both sides have some green units. Otherwise it will be the basic rules alone.
There is an advanced pursuit rule, very draconian. If your command (advanced rule) breaks an enemy command, it may pursue. If it does, the victorious command pursues off table and does not return. But at least it doesn't count against army morale.