The content of nutrients and bioactive compounds, and antioxidant capacity were assessed in the juices from two red-fleshed oranges, Cara Cara and Kirkwood, and compared with that of a standard Navel orange. Two juice extraction procedures, hand-squeezing and industrial, and two treatments, pasteurization (85 °C/30 s) and high-pressure homogenization (HPH, 150 MPa/55 °C/1 min), were evaluated. For most of the nutrients and bioactive compounds, the hand and industrial juice squeezing rendered similar extraction efficiency. Individual composition of carotenoids in the juices were differentially affected by the extraction procedure and the treatments, but the red-fleshed orange juices contained between 3- to 6-times higher total carotenoids than the standard Navel juices, being phytoene and phytofluene the main carotenoids. The industrial and treated juices of both red-fleshed oranges contained 20–30% higher amounts of tocopherols but about 20% lower levels of vitamin C than Navel juices. Navel juices exhibited higher hydrophilic antioxidant capacity, while the red-fleshed orange juices showed an improved lipophilic antioxidant capacity. The main distinctive characteristic of the industrial juice by-product of the red-fleshed oranges was a higher content of carotenoids (×10) and singlet oxygen antioxidant capacity (×1.5–2) than the Navel by-product.