To get the best video quality, it's usually best to send digital data (HDMI). Modern display devices are digital, as is the signal coming from the disc. The player has to convert that digital signal into analog so it can output S-Video and Composite signals. The display device has to reconvert an analog video signal into a digital format so it can up-scale the incoming image to the screen's actual resolution.
However, you have to use an analog video connection to get closed-captioning, if you need or want that. HDMI audio is transmitted during the "Vertical retrace interval", which also is when the closed-captioning text is transmitted. Having one prevents having the other. Closed-captioning text usually is different from the subtitie tracks provided on DVDs.