Neither is going to take up a whole day. You might take a look at videos on Youtube that various tourists have made to see what each peak is like.
There is a view over the whole city from Corcovado, out to the beaches of Zona Sul, plus the statue itself. You can go up on the train or by van. (Sugarloaf has a somewhat more limited vista of the water below, but a pretty one, and a longer view over to Corcovado.) The statue is really just that, on a fairly small viewing platform. Some other tourist can take your photo with arms outstretched under the Christ's, and you can try to identify city neighborhoods and landmarks. Sugarloaf is actually two peaks, two cable car rides (with Morro de Urca the first, and Pao de Acucar the second, the tallest). You can also wander around the top of Urca and then take the second cable car up. If you get off the asphalt path on the top, you can see the little monkeys in the trees and buzzards soaring by at that altitude. The Urca neighborhood at the base can be explored too.