1x GTX560 Ti > 1x HD6870 by a visible margin.
1x GTX560 Ti > or < 1x HD6950, depends on the games.
1x GTX580 > 1x HD6970 any day, even the price is GTX580 > HD6970.
plus you could grab another GTX580 or HD6970 to make it a dual card too... bah, stick to one card, saves you the headaches from problems and if multiple cards scales well on the games you're gonna play. common problems are if theres enough space between the GPU so it could suck air to cool it self, if the games you'll play scales well with multiple cards, micro stutters and so on.
not gonna play games? stick to onboard.
picking a stronger card depends on the resolution of your monitor, anything equal or below 1920x1080 you`ll only need 1(one) GTX560 Ti or HD6950.