A unit of Yankee infantry was about half of what a Confederate unit was in size. A Yankee Brigade was about 1500 men, three 500 men regiments. The Yankees had more officers to go around than the Confederate Army. A full sized Confederate Brigade( a rare thing) was 3000 men; three full sized infantry regiments of 1000 each. Not sure if cavalry was the same.
Not according to this site.
http://www.angelfire.com/wv/wasec5/formations.html
Each Union or CSA infantry regiment was made up of 10 companies, each (theoretically) of 100 soldiers.
There was some difference in cavalry regiments, apparently. A Union regiment had 12 troops of 100 men each, while a CSA regiment had 10 troops.
Throughout the war, and on both sides, there were also units that varied from this ideal, even in theory. In practice, as stated, regiments very often were 50% to 80% under-strength at any given time. I believe CSA was more likely to assign new recruits to an existing regiment than was the Union, making their regiments larger, as you say, on average.
Here’s another link. It claims Union heavy artillery/infantry regiments also had 12 companies.
http://www.civilwarhome.com/armyorganization.htm
According to this site, while Union and CSA regiments tended to be about the same size (always in theory), formations above the regiment level tended to be larger in the CSA, presumably because CSA brigades and divisions had more regiments in each.
http://www.civil-war-journeys.org/military_terms.htm
As you can see, there’s more than a little difference of opinion out there on the subject.
In the famous charge of the 1st Minnesota at Gettysburg on July 2, there were 262 men in the regiment, with two companies on detached service.
215 of them were killed or wounded in just a few minutes.