Running two feeders to one building for electricity is silly -- you can get the job done with one.
There is basically no reason in this day and age to run multiple feeders to a building in the fashion you are describing. Even if you are using multiple subpanels, you can have all of them fed from a single feeder using the feeder tap rules in 240.21(B) -- both (B)(1) and (B)(5) apply to your proposed application.
In a typical setup for this, the feeder conduit runs up to an auxiliary gutter (if you can't find an aux gutter, it's really another name for a wireway -- think fiddle vs. violin). This gutter runs over the top of the panels physically and contains the tap splices (think screw lug terminals), while the tap conductors run through conduits down to their respective subpanels. You do need a sub-main in each subpanel to do this though, but consider it a small price to pay for only having to pull once.
As to wire size -- the taps can be sized to match the sub-main overcurrent protection devices provided they're more than 10% of the size of the feeder being tapped, while the feeder itself should be sized to provide the needed ampacity to both subpanels.
Also, the panels need to be next to each other as this setup technically falls under the "rule of six" in 225.33 (this is 225.34).
Don't tear out the other pipe if it's already there, though
However, if you already have the second conduit trenched in, leave it there! It's handy as a convenient place to stuff phone, network, CATV, or other sorts of low voltage wiring, and you can simply reroute its ends to go wherever they need to with some conduit work.
The conductors will have to be full size to the 200A breaker. Remember what protects the conductor is the 200A breaker if you reduce the conductor size there must be an additional breaker to protect the the current carrying conductor. NEC does allow for the feeder to be reduced for the final 1/3 distance of a feeder which is probably impractical, but it does allow the subpanel to have 150A buss.
Best Answer
Since this is fed from a breaker in your main you can do it with both wiring methods but it would be considered a feeder and the wire size would need to be good for 125% of the breaker or 125A the way I interpret the code. If all the loads are non continuous it could be 100% but with all those spaces there will probably be a few continuous loads so better to be safe for the long run.