Removed quests and cut content are two different things.. Siege battles & who takes part in them were cut to save time, whereas the quests were removed as a change to the story. The only thing cut from the Civil War were who does the speeches, npc's that take part (Giant's for the Stormcloaks), and citty siges (Markarth, Falkreath & Morthal). This started from someone saying the Jarl just sits on his throne all the time.
Not really, cut content/removed quests are basically the same thing. They were quests which were cut. The Civil War is a quest, and had several quests removed. There were 12 radiant quests + the city sieges. Only three quests remain in the Civil War out of the 12.
There was a lot cut from the Civil War.
Imperial Legion quests
"First off, we've learned the location of some rebels scouting our positions throughout the hold. Need to take them out."
"First off, they've got some rebels holed up in a nearby settlement. Need to clean them out so our boys can move in."
"First, we need to limit Stormcloak capacity and send them a not so subtle message by sabotaging a resource they claim to control."
"First, we have information regarding the movements of a rebel courier. We need to intercept him and confiscate his package."
"First of all, one of our men was captured by rebels who refuse to surrender him. So we're going to break him out."
"First of all, I need to sew confusion and doubt through the rebel troops. I want to assassinate their commanding officer."
"First, our intelligence suggests one of the rebel garrisons has become disaffected. If we play our cards right, we should be able to turn them."
"First off, seems the Jarl's Steward might be vulnerable to blackmail. Need to investigate that possibility."
"First on my list, is a problem with our supply caravans being constantly harassed by a giant. Need to deal with that hairy brute. And soon."
"First, I need to get a handle on rebel operations. Need to discretely liberate some documents from their headquarters."
"First of all, I'd like to drum up some more support from the local populace. I have someone in mind."
"First off, there's an Orc hanging around causing me headaches. Something about a vision quest he needs help with."
The dialogue is doubled with "Secondly" so it appears you got given two assignments.
The enemy faction would also actively play against you, attacking your Holds, villages, and what not. You were paid weekly and could donate your money to the widows of your fallen soldiers. If I recall correctly you were able to set patrol routes for your soldiers. Attack and take over mines, mills, farms etc.