Mark. I had the same experience while switching from my D7000 to D800. My D800's buffer was expecting high performance from my cards; which I thought could deliver; but they didnt. They were still 95mbs cards and still the buffer was holding me back.
What cards are you using right now? Lexar 1000X UDMA7 did wonders for me. Thanks to Dave; Those are very fast.
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http://www.bhphotovideo.com/c/produc...mory_Card.html
He sent me a chart with speed tests with my camera for every brand of card out there. They didnt test the 6D yet, but 5Dmkiii should be very similar.
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http://www.robgalbraith.com/bins/cam...cid=6007-12452
Hope this helps.