by both sides in the Civil War
Not precisely correct. While indeed a draft was called during the Civil War, it was not by any means the main source of manpower for any side.
According The Origins of the Civil War (Duane Cummings and William White, Glencoe Publishing Co., California, 1972), most of the people who were drafted by the North never really turned out to serve.
They present the following numbers:
From July 1863 to May 14th, 1864, 537,672 recruits were obtained by the North. Of these, approximately 489,000 people were volunteers. Slightly under 13,000 were actual draftees, and the rest were a variety of hired substitutes for draftees.
On July 18th another call for troops was issued, and 272,463 troops were brought in. Of these 188,172 were voluntary enlistments and 26,205 were draftees (the rest being substitute).
The final call was issued on Dec. 19th 1864m obtaining 187,092 troops (of them, only under 7,000 were draftees).
A similar picture was witnessed in the South.
It was the Continental Army of General Washington that won the war,
That is an issue of division among historians. Morrison (he of the Oxford History of the American People) seems to think seems to think that it was the Carolinas Campaign(different from Shermans campaign some years later), not Washingtons exploits, that proved decisive in defeating the British. Second, it was the British, under most accounts, who possessed the more disciplined, professional military, and look where it got them.