They were intended to be. Confederate currency was patterned to be very similar to US currency at the time, right down to the green color. (There is, by the way, a bunch of fascinating analysis about Confederate self-image based on what they put on the currency and about the production itself, which was difficult). It usually said something on top similar to, "redeemable six months after the ratification of a peace treaty between the Confederate States and the United States with 5% interest." This points to the first difference: Confederate currency was not the gold backed currency of the time but a debt instrument. The interest was intended to make up for the fact the Confederacy had no gold reserves. Later on, the interest went away, but it was still understood to be later redeemable.

Nevertheless, Confederate dollars were supposed to be worth a 1:1 ratio. And they were fairly close, at first. A Confederate dollar was worth 90% of a US dollar at the start of the war. Its value was based on the entire Confederate project, though, and as the nation's fortunes declined so did its value. By the end of the war, it was worth about 2%. Most of that drop came in the first two years: by 1863 it was worth about 6%. After 1862 the Confederate economy increasingly slid into a crisis from which it wouldn't recover until long after the war.

Confederate dollars were never accepted in the North in a widespread sense. Some Confederate soldiers took supplies by force from Northerners and paid in Confederate currency. The US government actively acquired Confederate currency for a variety of wartime purposes. Some soldiers captured Confederate currency as booty and would use it to buy anything anyone would sell (because they considered it to be worthless). But walking into a store and offering to buy in Confederate currency was likely to get you laughed out, or reported. Most damningly, smugglers mostly didn't accept them except very early in the war. Smugglers, whose entire business model included doing business in the Confederacy.

Union dollars, however, were used in the South for most of the war. In the immediate period after secession, greenbacks continued to circulate. After all, it's not as if everyone threw away their currency. The nadir of this was in 1861-2, when the Confederate currency and cause were relatively strong. The greybacks (which were also green but named greyback for the Confederacy) increasingly began to circulate. They pushed the greenbacks out of circulation extremely quickly, as economic theory predicts. Bad money, as they say, crowds out the good.

During 1863, as the currency increasingly collapsed, few people would accept Confederate currency. A series of alternative currencies popped up, from states and even companies. But none of these met widespread success. The gold standard remained the greenback (which was actually on the gold standard). It was the safest bet by far: if the US won the war, it would be the local currency again. If the US lost, it was still possible to redeem the currency for gold once peace was achieved. The Confederacy increasingly became a barter economy as the currency collapsed but the dollar remained good in the South. Even the Confederate government sometimes accepted it. On the front, Confederate soldiers would often accept payment in greenbacks but Union soldiers generally would not accept greybacks.

From Confederate Paper Money, A Shattered Nation: the Rise and Fall of the Confederacy, and Financial Failure and Confederate Defeat.