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Unfortunately, Cisco doesn't always clearly document the bandwidth of the chassis backplane itself. As an example, the 6500-E chassis supports more bandwidth and power then the non-E chassis, but neither was well noted until Cisco released the sup2T or the larger (e.g. 8700W) power supplies.
Right now, the sup2T provides a 2 Tbps fabric, but the chassis and/or line cards may restrict how much of the fabric bandwidth you can utilize. For example, a 6500-E with 6900 series line cards have 80 Gbps per slot, so to take full advantage of the sup2T's 2 Tbps, you need a 6513-E, 13 slots @ 80 Gbps * 2 (duplex) = 2.08 Tbps.
That noted, on the bandwidth issue, NDA might still restrict me in what I can say, but the 6807, if the fewer slots is acceptable, is probably (cough) a better long term investment.