there is no easy answer to this. there SHOULD be but its more complicated than it is for computer monitors.
lets start with computer monitors. you ALWAYS want to drive them purely digitally if you can help it. an lcd is internally pure digital. your computer data is pure digital. there is NO good reason to convert digital to analog, carry that data over a lossy cable and then convert BACK in the lcd to digital. totally useless set of D/A and A/D conversions. with dvi (digital) you get dot for dot perfection and also lack of need for many screen adjustments (most are now non-adjustable if you come in via digital in's on an lcd).
now lets talk about tvs. tvs are problematic due to the content quality being ALL OVER THE PLACE. and I don't mean this in a good way, either ;(
if we were talking about display text and flash (object based) graphics then a pure digital display would render them best. but we have poorly video taped shows, poor color balance, poor lighting, poor focus, and worst of all, poor analog to digital conversion - jaggies, blockies and hatchies galore! ;(
so here's my approach. the 'digitalness' of the blockies is too much for me to take. yes, technically the tv set is showing you ALL the data without any conversion stages but in this case, we DO need a missing state. a smoothing circuit. going pure digital often makes the video VERY harsh. but if you go thru s-video (yuk) or component (aaah!) then you get almost as much bit-for-bit data as hdmi but you get a bonus smoothing effect that helps low-pass cut some of the digital harshness that mpg encoding (poorly done) and bit-starvation does.
hope that made some sense. its counter-intuitive and experience based. I never would have thought this way until I experienced it firsthand. I was all for a pure hdmi connection (afterall, I INSIST on all my audio connections be spdif, which is digital) but the poor CONTENT quality of 90% of SD, about half the DVD's and even half the HD over satellite - they all need a better smoothing and deartifacting stage. using an analog middle stage is an ugly hack to deal with it, but its often better than a pure digital connection.
odd how that happens, huh?