In the Modern Era, are you setting your military units to Alert <A>, Do Nothing <Spacebar>, or Fortify <F>? Fortified units are better when you have a known enemy presence. The unit will not prompt you for new orders every turn. That way you command only the units which actually need orders. Makes things much faster.
Also, with your cities, create production ques and end them with research/wealth. Means less micromanagement. Or better still, leave them as puppets and let them do their own thing.
I actually quite like Industrial and Modern Era combat. it tends to be much more dynamic and has its own flavour. Tanks are a bit more mobile than mounted units, and infantry are much more robust. Things do get a bit static with Artillery. But, when bombers and rocketry come on scene all this changes. Things get much more mobile in the Modern Era.
Many of the mechanics of Ancient Era combat are still relevant in the Industrial Era. Such as using Melee AoI to protect ranged units. So instead of Swordsmen and Archers, it is Infantry and Artillery. Tanks function much like Cavalry, and AT guns are your new Pike/Spearmen.
For me, not much happens in the Ancient Era. My first foray into combat usually happens with Musket and Cannon, in the Renaissance Era. My economy blooms in the Industrial Era and this is when my plans for world domination come into fruition. By the Modern Era, I have advanced from 6th place to 2nd or 1st, and this is when I strike with finishing blows.
In modern combat, the total conquest of entire regions can be very dynamic. You have to think like Alexander the Great. With the "Hammer and Anvil". Technique. Your Anvil is your static standing army. Consisting of Infantry, Artillery, AT, and AA guns as required. When your Anvil is properly set, and fortified of defensible ground, it is hard to dislodge, and impossible to assault without heavy losses.
Your Hammer is your mobile force, consisting of Tanks, Paratroopers, Bombers, and Helicopters. As always, you take up the front, and choose the best ground with your "Anvil", and let the enemy forces come to you. Then you use your "Hammer" to strike killing blows when the enemy is weakened. Or manoeuvre to create entrapment scenarios, between the "Hammer" and "Anvil". Or use it to take an objective (such as a city) while the enemy force is engaged with your "Anvil". Once you get good at Modern combat, you will enjoy it.