2 separate rigs with 1 5970 each or 1 rig with 2 5970's

[Pipesnake]

Other than possible downtime, is there any benefit to either setup?

(One or both will be dedicated.)

[leepfrog]

Duplicate power consumption for mainboard/cpu when building two rigs (which might be around 50-150 Watts)

[Genrobo]

Two separate rigs would probably have better temperatures per card making them last slightly longer?
Negligible difference there.

You'd save on costs 'usually' by building a single rig, but given supply of boards/power supplies it might break even either direction.

[bullox]

Less costly to build a double.   Up front costs obviously include 1/2 price on Mobo, PSU, HD, Case, etc.  Ongoing costs about 30% less total wattage due to no extra mobo/hd/fans.

Make sure your motherboard will aptly handle 2 double sized GPU's though.  And make sure you are able to cool it correctly.  Try for under 60 celsius, be happy with anything under 70.  You will get more life out of the hardware.