If your tuner is one of the cheaper models flooding the market, their picture quality is inherently low and there's not much you can do about it.
They have low resolution outputs and also, technically speaking, the RF and IF sections will have poor bandwidth and phase characteristics resulting in poor analog signal quality even before it reaches the A/D converter that interfaces with the rest of the computer. A high-grade tuner will cost much more.
I haven't tried capturing such a tuner's output with a gfx card, but I doubt you'd see any improvement. Basically you'll need a card with VIVO (video-in-video-out). If someone who's actually used it this way would care to share his/her experience....?